I’ve played plenty of chess on iPad/iPhone and haven’t had the issue with the screen sliding during moves. The only time it happens is if you don’t actually grab the chess piece, then the device interprets it as a screen swipe instead of a move. In bullet chess every second matters, so it’s easy to slip, but if you make sure to tap the piece first and then drag it, the screen won’t shift and you won’t lose time.
As for the idea of subscribers being able to switch to “guest mode,” I don’t really see a benefit. If it’s just about practice games, you can always play against guest accounts directly.
Your suggestions are thoughtful and I can see why you raised them, but from my experience the screen issue comes down to technique, and the guest option isn’t really necessary.