Ah, thanks! I think I had a hunch that it's always beatable but it's good to have confirmation.
Adding a basic score/number of moves counter might be interesting. I realize some (all?) of the games are either you win or you lose, but having something extra to optimize might make replaying the hanoi solitaire more fun. It could also give a reason to move an alternating-suit stack, which felt like a unique type of move compared to a regular Towers of Hanoi, but doesn't have much purpose in the game as-is. It's a fun variant conceptually, but there's no lose state and playing it is pretty algorithmic :)
It's got me curious if there's a variant that would push the balance towards feeling a little more like solitaire. Maybe allow the offsuit descending stacks to be non-sequential, but go Klondike style for the empty slots and only let kings move to them?
Either way just some thoughts I had while playing it. Love the game, it's all really playful and creative!