Thank you for taking the time to write such detailed and helpful critique! For a post-jam version we should explore better movement options, and see if it's possible to implement an undo function. Andy is pretty handy with all that stuff so I'm guessing he would want to try it.
The reason you can only move over the hole when you're the correct shape is to limit movement on the entire playing field, we could have done that in different ways but it was basically for level design purposes.