What is 'correct' corner permutation after doing a 2x2x2?
What moves are allowed to extend the 2x2x2 to a 2x2x3, while preserving correct corner permutation ?
P.S. Cool answers to this questions will make for a new ZZ-d style 2x2x2 method.
Correct corner permutation after the 2x2x2 is when all the corners are in the right spots. You can then do the normal three move edge inserts without disrupting corner permutation. The only annoying part comes in EO where you want to have 0 or 4 bad edges since M' U M and M U M' are the Easiest edge flips that don't screw up your CP. This is actually not hard to force if you're good at influencing EO while inserting edges for the 2x2x3. The way I see it right now, the only hard part is going to be finding an efficient way to see a CPblock solution during inspection.