We can choose to assume the earth-dome above is stable. It's not clear to me that it would be, but we can take it as given. Actually, we could also pretend it isn't stable and slides/spins/crumbles away. In either case, a possible solution for several problems is to
build a geodesic dome along the boundary
(or whatever part of the boundary is not taken up by the earth-dome, anyway.)
Let's break this into two parts. First, we'll ask what it would take to build this. Then we'll ask what it gives us.
What would it take to make it?
Normally, a geodesic dome needs to support its own weight all the way down, and would require all the engineering that would go with that. But Evermill's gravity-boundary gives us a unique situation: if the dome would begin to collapse, the parts of it that are pulled into the sphere of inverted gravity are immediately being pushed back up by their own weight.
If it were built of rigid members, each of them that lies along the boundary would be pulled down and pulled up simultaneously--applying the torsional effect that will drive your free-energy flywheels--but also effectively giving each such member neutral buoyancy. And, in absence of external forces, they would tend to find that balance--in falling, more of their weight would lie in the inverse-gravity zone; in rising, the opposite.
But we don't even need rigid members. We can build the dome out of rope.
- Consider a circular rope, running all the way around the boundary, at about 45 degrees up from the ground. If it can't stretch itself wider, then it can't simply fall down on the outside--it's not wide enough. Maybe it would fall down one side, pulling the other side up?
- Well, then, anchor it with vertical ropes all the way around. If one side would come down, the other side must come up; but it can't because it's anchored. But wait...isn't the horizontal loop now bearing the weight of all the vertical ropes?
- Nope. Or not for long, anyway. If the ropes were cut properly, to fit the distance along the edge of the boundary, they'll also get pushed up as soon as they begin to sag, and find a position of neutral buoyancy.
- Since every part of this construction is supporting its own weight by straddling the boundary, you can add as many loops and verticals as you want...and the more mass you add, the more stable it becomes against the addition of the extra mass of (say) a person climbing up or down it, or any system of pulleys, or slides, or zip lines, or whatever transportation we'll eventually affix to it.
- What we have now isn't really even a "geodesic" dome...it's just lines of longitude and latitude. Normally, this would be problematic, even for a stucture with rigid members...without triangles in the structure, the dome would be vulnerable to collapse by twisting sideways one way or they other. But, as we've already established, this dome simply can't collapse. And having horizontal ropes (or rigid members, up to you) will be advantageous, as we'll soon see...
But there you have it. Technology required: Rope. Or wooden beams. And the ability to cut them at specified lengths. Method of construction is left as an exercise to the reader, but once you've got one rope to the earth dome, the second should be easier, etc.
What does it give us?
- First and foremost, it gives us easy access to the underside of the earth dome. You can imagine any kind of stairs, slides, firepoles, flywheel-powered elevators you like: the dome gives you a place to anchor them. If rope is too flimsy to hold your transport system rigid, upgrade the required parts of the dome to use rigid members. To go up, passengers take the inside of the dome. To go down, they take the outside.
- It also gives us a place to anchor more free-energy flywheels. If you build a circle of mills around the base of the gravity-boundary, that's a fair start...but there's so much more free energy to gain from utilizing as much of the open boundary area as possible. With your pseudo-geodesic dome in place, you can install spinning flywheels on every horizontal member that isn't occupied with transport systems or other usage. Chains or ropes can be routed up the vertical members to transmit power. (Mechanical transmission of power isn't the most efficient, but whatever you get is still free energy...)
- Finally, this gives us a way to anchor the earth-dome, if we'd rather it not rotate freely. I don't know what your plans are for it and what aesthetics you envisioned for Evermill, but at least on the practical side of things, maybe your commuters would like to have a reliable way to get to the same underdome-address every day.