how should I prove I own the game before itch just straight deletes it from my account?
They're not supposed to do that. Plus Innventure doesn't seem to violate new policies, we should be fine. But even if worst case scenario this game gets removed - it will stay in your library, and I'll probably be able to access stuff like customer info (I can check emails of people who've bought my game), so you can just DM your email address that is associated with your itch account and show me a receipt that was sent to your email when you've bought the game.
But yeah I'm sure everything will be fine and things won't go this far.