Do you know if that might be mitigated by using Chitchatter via a Tor browser? I’m still building my understanding of the low-level mechanics of WebRTC.

There are multiple reasons why TOR is not a good fit for WebRTC tunneling. However, TOR is already capable of establishing p2p connections via hidden services.

Pretty sure Tor browser has WebRTC turned off.

I didn't realize that. That's a bummer. =/