I like your idea, but upon testing it, unless I redirect the entire page to my host, the IndexedDB instance is not shared, despite the iframe hosted at itch.io pointing to the same site. This was surprising to me.
I'd rather keep the itch.io link stable. I think I'll cross my fingers that itch.io doesn't change the underlying iframe host they control. I use the Google Drive API to host saved games so that's also an option for players.