There's some principle that for a chaotic system, if the accuracy with which you can measure it is smaller than the largest perturbations you can make to it, you are willing to wait many Lyapunov times, and you have enough compute; then you can control the system. With this after a few dozens of millions of years you could control the small bodies of the solar system using relatively small thrusters and a big radar installation, and then put them all on aldrin cycler orbits to move momentum between the larger bodies.