Look, if you are concerned about your instance's IP address leaking out and your reason is "privacy" then I'm going to go out on a limb an say you probably should take about five steps back and ask whether you should be running an ActivityPub based server _at all_. At least one that isn't on Tor and/or that you haven't specifically hardened.
I also have to wonder what is the subset of people who are using cloudflare and for whom that ip address won't just be us-east-1 or some equivalent.