This is one of the best implementation of this idea I've seen so far. You've clearly put a lot of effort into solving some of the problems this puzzle idea has.
The addition of walls on the levels made it a lot easier to control the dice, while solving the problem of 4 looping infinetly. The UI is great, the result of each move couldn't possibly be more clear, and it made planning ahead a lot easier.
Also I loved the sound design. I know it's just ambience and some notes, but it made the game feel so much better.