Well this is all a lot of effort, there's far easier ways, proposed by Dyson himself, and improvable since then:
MARS
Problems: thin atmosphere, no core rotation to provide protective magnetic field, oxygen all locked up in rocks.
The atmosphere is easy to fix, you seed the planet with tonnes of bacteria that eat rust to liberate oxygen - such as the bacteria that have eaten the Titanic. You could even genetically engineer such a bacteria, or create a nanobot to turn the Ferric Oxide rocks into iron and oxygen. There's a caveat - the O2 levels must not rise above 20% or the planet becomes highly flammable. It will also need three or four times as much nitrogen, and some Carbon Dioxide, to create a self sustaining atmosphere and reasonable temperature.
The core is a bit trickier. You need to melt it, essentially, and then centrifugal forces and friction will take care of the rest. This is tricky, but may not be impossible.
Let me explain something here: Those people who say things are 'impossible' because 'physics says it cant be done', are usually wrong. This is because they base their judgement on the current level of knowledge. History shows that almost everything that has been declared 'impossible' at some stage has, in the light of later science, later discoveries, later technologies, been possible. if you think for one minute we are anywhere near a complete understanding of Physics, think again. There are VAST areas of science where we know nothing. And the areas of science we are aware of are mainly incomplete - both Relativity and Quantum Physics being two examples of theories with MASSIVE gaps in.
In 1890 it was declared 'impossible' to travel faster than 60 MPH as 'the air would be going past too fast to breathe'. In 1890 you could not possibly have foreseen airplanes, cars, rockets, satellites, lasers, computers, smartphones, the internet, relativity. quantum, physics, M theory, television, radio.... you would have had no idea of plate tectonics, Navier Stokes Equations, Genetic engineering, nuclear power, DNA, nanotechnology...in short, you cannot possible predict what is impossible, because you cant predict what we may know in the future to make it possible. (That include faster than light travel, BTW)
But I divert. In short, we can't get Mars's core rolling today, but maybe in 100 years we can pump enough fusion or antimatter power into the core to melt it. I'm confident we will crack the problem, since historically man has cracked every problem hes ever faced.
Venus has a similar core problem, and unsuitable atmosphere, but the solution is similar. The Runaway greenhouse on Venus is a consequence of the hydrocarbon atmosphere. Earth had a similar problem, until the Great Oxygen Catastrophe, when bacteria began producing masses of O2, breaking the Greenhouse grip. Read more here
https://en.wikipedia.org/wiki/Great_Oxygenation_Event
In short, we need hundreds of orbiting stations over Venus, mass producing and showering it with algae and cyanobacteria in a man made rerun of the GOC.
We still have the problem of the lack of magnetic field. Possibly we can build an extensive electromagnet to protect all or some of the planet until we solve how to melt and spin up the cores. It would not require a massive strength, but would need to be large to head off cosmic particles.
