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I created a puzzle on puzzling.stackexchange.com and the resonance is hmmm let‘s say moderate. Maybe in this forum there are some people who are interested in this little brain teaser.
Based on the comments under the question. (Isn't AxiomaticSystem one of the regulars here, under a different name?)
Start with superflip composed with checkerboard, then twist the U corners clockwise and the D corners anticlockwise. Then finally break up the matching colours with a U move.
The second question is about the minimum number of moves, which makes me think there's a simpler way to come up with a state without matching colours. Certainly, if it's a puzzle meant for humans, it shouldn't involve a step where you need to find optimal solutions for many different states then choose the minimum… I haven't figured this one out yet.
Nice idea for this solution! But I must disappoint you. The second question needs indeed computer assistance - at least I think so. But no programming is needed. There is a program out there which can do the work for you with a few mouse clicks.
I created a puzzle on puzzling.stackexchange.com and the resonance is hmmm let‘s say moderate. Maybe in this forum there are some people who are interested in this little brain teaser.