The quickest win would to move off of Heroku. Either rent your own server that you can control (to a reasonable degree), or find an alternative that doesn't suffer that issue.

Redis would work but I'd be afraid of race conditions. There probably wouldn't be any, but it's something to be aware of.

If you wanted to test the waters with at least the relative public, I'd consider doing step 1 of renting a server, but then hiding it behind a Tor hidden service. Inconvenient to connect to? Yeah. (Probably) safe from the Hasbro demons? Also yeah.