What I want:
A self hosted version of GitHub that is a precise mirror of an actual GitHub repository. That is, PRs from GitHub appear on the selfhosted instance and my reviews from the self hosted instance appear on GitHub. That way I can work on my private instance when GitHub is down (or slow) and I can be assured my work still appears to everyone online.
Does this exist?
Git gets you 90% of the way there. Sounds like you just want a decentralized review solution to go with it.