[llvm] Attempt to fix libc++ actions runner restarter. (PR #120627)

[Louis Dionne via llvm-commits]

https://github.com/ldionne approved this pull request.

The fact that we can't test that without pushing to `main` is horrible, but I don't see how we can best make progress on this issue otherwise.

If you push this, please carefully monitor the CI state for a bit cause this can easily cause unintended instability and we'd rather have something broken-but-in-a-state-we-understand over the holidays than something broken-in-new-fun-ways.

https://github.com/llvm/llvm-project/pull/120627