There's been many games of this type in the gamejam and if you watched the GMTK streams you probably heard Mark say that these games often just end up with trying to move around randomly until the puzzle is solved. Sadly I think this applies here as well. It's just the problem with this particular game type.
Than being said, I really really like your presentation. It looks amazing, starting from the intro screena all the way to the dice rolling and the end of the level. Easy 5/5 there.
Great job!