After 2 weeks mine just disconnected, so I guess compatibility mode doesn't resolve it. I was obsessively checking the RCS connection state, so I know the exact moment I was de-registered. It happened when I connected to a public wifi network that had restrictive settings and ports blocked, which prevented my VPN from connecting easily (had to use obfuscation). My guess is this wouldn't have been a problem if we could verify our numbers the way Google intends us to, but whatever is getting blocked by GrapheneOS caused it to get de-registered in this moment.
I've gone through the process again and reconnected. This time the RCS connection state has reverted back to "Transport: Chat API w/ RCS", instead of "Tachygram". I'm still curious to know the difference.