I choose a "meticulously deconstructed" variant. I call it the "onion method".
First, invent a self-replicating robot. It does not need to be miniaturized. It would actually probably work better if they were all stadium-sized. Allow replication, using solar energy and near-surface resources, until the entire planet is covered by a uniform layer one robot deep.
The robots then securely connect to their nearest neighbors. You now have a uniform robot tensegrity shell around the planet. The linkages expand until the shell rises to a uniform altitude above the surface. This likely requires a material with tensile strength higher than any currently known, and a material with compression strength higher than any currently known. I haven't done the math. Reasonable strengths may require that the shell robots run on the surface a bit to start the whole thing spinning faster than the planet.
A circular section of the shell directly facing the sun de-links, falls back to the surface, and begins replicating as before. The remainder of the robot shell opens like a jellyfish mantle, to catch the solar wind and reflect additional solar energy to the dark side of the planet. The shell sails to a different orbit, so as to not re-collide with the planet.
Repeat until all shells have sailed away.