They only do archiving. Hosting projects that are under development is not in their mission. https://www.linuxfoundation.org/ looks like a better match.

There is a need for an organization that is willing to host established but small and unfunded projects like libtiff, libpng, zlib, etc., and give them some minimal organizational backing in the interest of continuity (so no github). Somewhat similar to, but more general than, what the Network Time Foundation is doing for ntp and related projects.

I'm not saying you should do it or that it's the best option, but putting your code under the umbrella of something like the FSF or the Apache foundation comes with this sort of benefits.

A potentially brilliant idea. I wish I had a clue how to follow up on it. Perhaps someone else here might!

The Internet Archive would be the perfect group of folks to archive code.

Indeed. Updates in Github (which can create a webhook) should trigger an archive operation.

It has been on my list to integrate https://github.com/joeyh/github-backup with https://github.com/ArchiveTeam/ArchiveBot.

I love the Internet Archive, so it would be great if some kind of archiving function could be worked out. But if it's on GitHub now, it should be exported to Zenodo today, so there's at least one reference version around for Internet Archive to backup.