Very interesting, thematically and with the presentation!
I love the idea of you building your dice, then rolling for your actions, and then progressing through a level. I couldn't stop myself, though, from constantly just rearranging the dice to have what I needed.
A solid improvement, in my opinion, would be to restrict dice editing to only before a level starts and to roll the dice a few times to determine your "Action Pool". That would let a player decide what frequency they want, while still using the dice mechanics.
Overall solid entry!