Awesome visuals, very cool idea (pun intended), and overall fun to play! Sometimes I felt the ability to turn the dice on the spot was a bit too powerful. Especially in the earlier levels, you can make many moves without thinking and then fix the puzzle on the last two fields. Have you thought about making specific tiles on which the player can turn the dice or limiting the dice to only one turn per tile?
I love how you addressed this issue in the later levels by slowly introducing new mechanics that make the player think from turn one. The pacing is also incredible. Every time I had a realization that made the levels too easy again ("Wait! Those three fields always sum up to 7!", etc.) it took you at most two more levels to introduce a new twist/mechanic. Just enough so that I have time to feel good about my accomplishment and not get bored by the difficulty.
Another thing I noticed is that the levels are very linear. I always immediately knew what path I would take, the only question was how I would rotate the dice along the way. Was this intentional? I think it might also be interesting to have levels where you have to figure out which path to take as well.
All in all, you made an amazing game and I would not be surprised at all if I see you pop up in the announcement video of the Game Jam winners!