You can make a pose that moves several bones at once, but it would still take a lot of poses to cover all the possibilites.
If A:M had a scripting environment that supported bone movement you could make it identify all the cubes that are on, say, the middle level and rotate them all by the same amount around the center.
Hmmm, I wonder if an expression could do it? Expressions don't have any looping capability for testing all the cubes though, AFAIK.
But I'm still wondering why the white tiles didn't anti-alias. I can't imagine why they wouldn't.