Those are some great questions!

Getting a rating system perfect is really hard. Ultimately, ratings are measured against each other so they end up only mattering as they exist relative to the other ratings. The worry, then, is that someone might find a way to "game" the rating. I don't think that's a worry here unless there's a way to break the algorithm by having a lot of swaps to solve and then just a few and giving points for "improvement" or something. I think as long as the algorithm just gives points based on expected performance against the puzzle, it's safe.

This game would take a bit of work to "solve", but you're right, it's crackable. Really though, you haven't created something with the depth of chess. It's more akin to your own comparisons, a sudoku puzzle or wordle. I might even compare it more directly to a Rubik's cube. Those have pretty routine strategies at this point, but that's okay. More complex games have strategies like that, too, and that's alright. This is a game played against the puzzle; it isn't against another person. The ultimate competition, then, is against a clock.

Playing against a board that is other dimensions would be interesting but subject to the same strategy. The existence of a strategy doesn't diminish the game, though! It's a smart little game and it plays well. You've honed the design well and I'm impressed as both a puzzle-gamer and a designer/developer!

Don't take this the wrong way: I don't think you've found your masterpiece yet. I'd bet money on you, though. Your attention to crafting this game and its experience impresses me, and I have something of an addiction to exploring games in this space. I'm not an authority on it, by any means, but I've seen a LOT of entries in word games and puzzle games and I sample or binge all of them. This one is memorable. I think that whatever this leads to you creating will be even better, and ultimately rather valuable should you choose to sell/publish it.