already given your game a rating, just didn't leave a review.
So here it is: i think your game is too complex for me, that or either my brain is not compatible with this type of game.
However, as an idea, you've created an ingenious way to adapt to the requirements of the theme of this jam and i think it's nice to see original content in this saturated market.
I also am impressed by the auto-pathing which you created and carries working on even when swapping pieces around.
As a suggestion, whilst i do appreciate you've made the game purposefully like this, that the player needs to turn the puzzle pieces of the map around, and not changing the camera angle, i still think you should have had that functionality as well. It's never a good idea to not see the player character.
Over all, this is a well made game and a lot of consideration has been put into making it.