First of all, kudos for the impressive amount of puzzles and mechanics you've managed to pull off. Your game is visually compelling, I liked the mysterious sound and the concept is cute.
I think the major flaw in the game is actually coupled with the theme of the jam: the loss of control, in puzzle games, might be super frustrating **once you've solve the puzzle in your head**. More than often I found myself just waiting for the right character to show up, or almost getting to the right position before falling into a hole.
I think that it's not a fundamental issue: if the player had a way to improve the chances that a specific character would get nominated next, or maybe get to choose every other round, or perhaps if there were multiple ways to solve each puzzle... anything that would not make me just wander around until the vital character shows up. Maybe sticking to a grid could feel a bit more tight in terms of accidents, but that's a minor technical comment :)
Great job!