I took a break from this project, but I got back and overcome a couple of hurdles that had me stuck!
There is some sort of sine wave wobble now, which gives all the pieces unique shapes! As a result, piece collision boxes need to be more precise now, and I don't yet know how I will go about that.
I have also been working on adding a very simple animation that plays when you pick up a puzzle piece! The animation is in the game, but it doesn't look quite right yet (I don't know why).