I like the concept, though I don't know where you found four-sided cubical dice.
I will say, though, that the lack of an undo key did me in. On level 8, I'd maneuvered most of the cubes in place and then accidentally hit an extra "up" that pushed the red cube against a wall. All I needed was "X to undo"; instead, faced with having to do the whole thing over again, quitting felt like a better idea.