> I'd rather stay in Github and maybe use another service purely as backup.

Swap those two and you're on the right track. I think the best way to use GH is as a mirror for a self-hosted git instance, with or without web frontend. It gives you the reach of GH with the, dare I say it, reliability of self-hosted. It also gives you the chance to keep things off GH which you don't want to be there. Keep the self-hosted instance private for most things, use GH links for public access. When GH is down again you can always give people (temporary) access to your self-hosted instance if the need arrives.