A (Qualified) Defense of Habitable Dyson Shells
Habitable Dyson Shells in the 1-2 AU range seem a bit absurd from an efficiency standpoint. I'll be defending this as being a fundamentally tractable engineering challenge (without unobtanium materials or new physics), not as something we will actually be doing.
Intro: To Begin With, Build a Dyson Sphere
The first Dyson sphere we create won't be a habitable (or unhabitable) shell, but a solar power collector that beams energy to wherever we need it.
Surprisingly, we can get started on that with something close to today's tech -- ability to harvest a bit of fuel and mass from near earth asteroids, solar sails to get around, plain old photvoltaics, rockets, lasers, and (most crucially) self replicating robotic systems. Since manufacturing systems on earth are nearly self replicating over all (i.e. they do replicate, with human help), and since no particular step in the supply chain cannot be automated in principle, this is justifiably in the "near term" category, especially if we include robotic telepresence. So this is no mere thought experiment.
To take control of the solar system's available energy, the prerequisite for this grand scheme of a Habitable Shell, we'd probably begin by making a light-supported system with a density of around 0.78 g/m^2, aka a Dyson Bubble, comprised of statites (stationary satellites). This lets us generate (or rather, take control of) large amounts of energy, which we can convert to antimatter, high-intensity lasers, high velocity kinetics, and so on. Enough that we can more or less do whatever we want with the rest of the solar system, on a scale of years to decades.
We need to process about 200 quadrillion tons (200 exatons) of matter (the mass of Pallas, one of the biggest asteroids) to create this form of power collector if we want to do it near 1.0 AU. On the other hand, at 0.3 AU, it is closer to 20 eT, which is the mass of a medium sized asteroid. This seems to be far enough out from the Sun that we can probably engineer working systems without devoting excessive amounts of effort to cooling and radiation shielding. For mass, we can disassemble Mercury (which is ~300,000 eT), and have lots more left over (which can go towards producing large numbers of robots, habitats, and any other infrastructure we want/need in the mean time).
Energy wise, it appears feasible to disassemble Mercury even if we assume fairly dismal launch and construction efficiency. The energy requirement to pull a kilogram from Mercury's surface, given escape velocity of 4.24 km/sec, is about 18 MJ. Assuming that is being spread out to 0.78 g/m^2, the energy payback time (once you have converted it into solar collector) is only a little over a second! Also note that as we pull more matter from Mercury, the launch energy requirement diminishes, and the total gravitational binding energy is 1.8×10^30 J (an amount which could be harvested in a matter of hours if we had a whole DS).
The thin-film form of Dyson bubble might need more mature tech than we can get to right away -- such lightweight, fragile plates might be hard to control and so on. So there's the thought that maybe we would want to use thicker collection surfaces to begin with. Also there could be a lot of robotic equipment involved in fabricating it, which we might leave in a more traditional orbit rather than spreading it over the whole sun. So maybe we need to start out with 10g/m^2 or so, set up a slightly offset Dyson "ring" (with reflection angle used to modify the orbit of each component slightly so we can spread them out and ensure they never block the light from the earth). In that case, 18 MJ launch cost results in 100m^2 of collection surface, which takes more like 20 seconds to pay for itself. Not really a big deal even so. In fact, we can posit substantial efficiency losses (assume we need 100 times that much mass for the manufacturing robots, etc.) and still make progress on the sphere as a whole in a matter of weeks or months.
The next phase in my mind, after a few months to decades of disassembling Mercury, or partway through that process, ends up being the development of a Saturn-like ring consisting of Mercury's mass mostly converted to asteroids, a razor thin line as seen from earth, with the major solar energy collector systems stretching north and south along the sun's equator (remaining out of line-of-sight from the planets), just far enough to harness 1-10% of the total solar energy. This collected energy gets beamed to sites within the ring that are optimized for reception.
The ring (which I think of as a "manufacturing belt", being 20 times as massive as the asteroid belt and far denser, but still fairly diffuse, and populated with a large number of self replicating robots) could be a decent place to live. Habitats with people in them can be set up to be shielded from radiation with several kilometers of rock, with smaller structures on the inside for gravity. However, really the only reason we'd want people out here is in case some tasks require active telepresence, so we can get to sub-second response times. If too many tasks need human oversight for too long, the project eventually hits a bottleneck until we can either reproduce our way out of the problem or automate them better.
Finally, at some point the manufacturing belt starts churning out a large number of lightweight graphene-reinforced panels that can float over the polar areas. At this point, we can cover the whole sun fairly quickly.
Creating a Shell
Now that we have a whole sun's worth of energy to play with, plus an obscene number of high throughput manufacturing systems capable of self replication, it's a matter of getting enough of the right materials into a shell.
Jupiter has plenty of matter, but as noted it's largely hydrogen. We might have to move Jupiter (or it's atmosphere) out of the way to avoid gravitational stresses on the sphere. Whether we can transmute the materials of that atmosphere to solids within a reasonable time is open for question. One thought is that, if we can get enough carbon together, we might be able to encapsulate "bricks" of highly pressurized metallic and/or liquid hydrogen within smaller shells of diamond or graphene, which can work as building blocks. It should also be possible to contain large stocks of pressurized H2 inside a series of smaller rocky bodies held together in spherical shapes mostly by their own gravity (gravity balloons).
In any case, if stick with the inner planets, we can build a shell a few centimeters thick (42 g/m^2). This shell could be held in place using ion jets, kinetic slugs, and so on, temporarily, but is nowhere near thick enough to hold against its own weight as a shell if we assume it's made of standard materials. Luckily, holding against its own weight isn't actually going to be necessary. We can instead create a system of strain relief mechanisms that use various forms of energy to hold it in shape.
Strain Relief Mechanisms
One simple mechanism to consider is kinetic. A series of "tracks" could be mounted throughout the sphere, upon which high velocity chunks of matter (steel, for example) are moved around very rapidly. Niven's Ringworld actually spins fast enough to invert the equation and produce a gee outward, however we really only need a small fraction of that. A set of giant rings that exert outward pressure by spinning at over the natural orbital velocity could be imagined. However, it should be equally possible to use much smaller structures instead.
The total lateral force needed to make sure the structure doesn't collapse is not that much per square meter, the issue is that it needs to be enough to counteract the pressure of gravity upon each local area (which is slight). One possible way to do this would be to set up a series of circular loops, 1km or so in circumference, and induce momentum enough to produce a few gees on the weights contained inside (which could themselves be circular). They would impart constant pressure to the track, via magnetic levitation.
Another mechanism to consider is optical/electromagnetic. As with the solar collectors, 0.78 g/m gives the relationship between normal solar intensity and the sun's gravitational influence. Going to an average 42 kilograms is 5000 times as much. But as long as the light pressure is being used for pressure alone and not to alter velocity, it's not used up, so multiple reflections may be used.
We don't necessarily want to try to reflect too much light from the habitable area directly, but we could imagine a set of platforms comprising 0.1% of the inner surface area that reflect the sunlight 5 million times or so before exhausting it. At 1 AU, that's 5 gigawatts. A bit much, but maybe worth considering with a very efficient reflector.
A better way to do it might be to cover the whole surface with strain relief structures that reflect light laterally, instead of shooting it across the sphere. For example, every kilometer or so, there could be a series of lightweight fins sticking out the outside, designed to reflect light back and forth and transmit the pressure to the structure. Light could be slowly fed in from a laser, and allowed to escape after many reflections. The fins could be much larger than the area they protect, for example 10 km long for 1 km of separation. That reduces the radiation density they handle to 10% or 500 times that of the sun for our 42 kg model. The mass of such fins could be much lower than that of the shell, since they would be very thin.
There's another radiation mechanism to consider similar to the above, but it dovetails with a cooling mechanism, so see below.
A final strain relief source to consider would be magnets. This can be either diamagnetic materials sandwiched between permanent magnets, or permanent magnets oriented so as to repel from each other. This has the virtue of simplicity, and I can't really think of a down side.
If we decide build at 1.0 AU, it's going to be too hot if we can't rapidly cool the outside of the shell. The physics imply that there's no way to cool faster in a vacuum, other than to increase the effective surface area. One way to do this without increasing the sphere size is to string out a long tether made of carbon nanofiber, or something else that has high thermal conductivity per unit mass, every so many kilometers. What ends up happening is that each tether radiates heat in infrared form along the way, then reabsorbs the same heat again from neighboring tethers. This puts considerable light pressure upon the tethers, causing them to "fall" in the opposite direction of the sun's gravity, sort of like a balloon.
So you can string lightweight tethers out quite some ways -- multiple AU, perhaps. There isn't really much of a limit, since the light pressure from the infrared is greater than the solar gravity, and the tether's own gravity isn't very substantial. If the pressure gets stronger than the tensile strength of the tethers, the tether can be made thicker or mass can be distributed along it.
Another way to deal with the thermal energy is to transfer it to matter, move the matter out to a distant point, then move it back again. Hydrogen has a good specific heat density, so we could imagine a system of balloons filled with hydrogen which venture to the outer solar system to radiate, then return after reaching cryogenic temperatures, and reinflate/rewarm upon contact.
Effects of Size
The OP suggests that 1.7 AU would not receive enough light for agriculture. I doubt that will be an issue. First, plant life could be adapted to need a little less light. Many plant species would survive fine (if growing more slowly) under 1/2 to 1/4 the light. Second, we could set up a gossamer bubble that reflects light half the time and transmits the other half, so as to produce a day/night cycle with twice as much light in the day. Third, we can use fluorescence to convert more of the radiation to visible spectrum. Finally, note that a large amount of visible spectrum light would naturally be reflected by the part of the sphere on the other side of the sun. So all things considered, a much larger sphere should be more reasonable than a 1.0 AU.
The Problem of Gravity
This is the biggest issue with the whole idea. Solving it with a centrifuge is inelegant, as you don't get to use the inside of the sphere as a landmass that way. Moving to a white dwarf has the issue of not being the problem we are trying to solve. Moreover, gravity as we know it just doesn't work for the inside of a sphere. So we need more of a "clarketech" solution to make sure people fall to the floor and sustain a breathable atmosphere.
Fortunately, an idea that works for this purpose has been thought of that breaks no known laws of physics: Utility fog.
Utility fog is a system of microscale robots, which connect to each other using an octet truss configuration, with extensible arms and graspers, all too small to see. With careful programming, you can use them to simulate liquid, gas, solid, and weirder things still, i.e. gas that you can fly through, liquid that you can breathe. What we are interested in is something like the buoyancy effect of water, but made to run in reverse, so instead of floating, it pushes you "down".
Now, that effect alone might not be enough to fool your body. But the inside of your bones and even the matrix between your cells can be threaded with appropriately programmed foglets or comparable micro/nano systems. Thus, the effects could be very close to natural gravity as far as biology can tell, including the prevention of weakening of muscles and bones and the maintenance of normal appetite. As an added bonus, such foglets could be programmed to turn gravity "off" whenever you decide to do so.
Utility fog is a good setting for stories about "magic", since it's pretty flexible. But if you use it this way, remember that it has limitations: For example, you can disintegrate it with heat, and it has finite strength. (Aluminum oxide is preferred over carbon, since we don't want it to be flammable. However, it still obeys the physics that say very small things can be heated up very quickly.)
Another idea for pseudo-gravitation would be to imbue all life with magnetic particles (hematite, say, or maybe some rare earth nanocrystal that works better) and use a magnetized sphere. Since we're considering magnetic strain relief mechanisms anyway, it could make sense. Maybe both systems could be used by different factions on the same sphere -- the magnet people could be those who evolved in an area where the utility foglets broke down, or something like that.
The kinetic strain relief mechanism above might be adapted to become a series of ring-style habitats (actually, you could do away with the shell and make it a set of conjoined rings, each containing a magnetically coupled, spinning habitat that balances out the gravitational pressure). This would give you far less surface area to play with, but some authors might find it more plausible or interesting than programmable nanobots.
Scientific Advancement Rate
The kind of advanced nanotech (nanorobotics) needed to produce utility foglets is, well, not here yet. Perhaps we need hundreds of years to break through using the current set of laboratories and scientific instruments.
However, if we had trillions of physics laboratories working in parallel, trillions of computers crunching the necessary math, and so on, it becomes harder to rule out rapid breakthroughs. We could also run new kinds of experiment with tougher materials, higher pressure conditions, exotic matter, and so on. So the assumption that we wouldn't make various advancements within years of the first DS is grossly conservative.
Nonetheless, mostly, we just need to intelligently apply what we already know. For the issues mentioned here, as far as I can see, you don't need new science to work around them.
There's a lot of story potential in the Solar Dyson Shell Habitat idea, and it at least can fall under the auspices of hard sci-fi, though smaller habitats have more actual likelihood of happening. The prerequisites are thinkable, and not as far in the future as is generally assumed -- it is primarily a matter of having a self-replicating industrial infrastructure, properly organized, which makes use of space based resources. But it also takes some creativity and understanding of the obstacles.