Nah, that's too smart of a behavior. What exists now may have some edge cases, but it is otherwise staright-forward and intuitive. The only real "hassle" is swapping two large assembled pieces closer to the end of the game round, but it's not really a hassle. Not a big deal, really.

Yeah, I’ve heard that from a few people.

I’m thinking of adding a “shuffle” button to rearrange the tiles if you get really stuck. It’s theoretically possible to get in an unwinnable state where you can’t swap two tiles

Perhaps do what you showed at the link, but only activate it on long tap-and-hold?

That is, if you hover a piece over some spot for X seconds, then it will shuffle other pieces out of the way.

I like that demo, looking forward to seeing what you come out with.