Why not just host it yourself then? You can get precompiled gzip and sane caching. The only reason I can think of to use GitHub Pages is not wanting to pay for a proper host.
Having used GitHub Pages, S3 and my own VPS for hosting, a homebuilt host is by far the easiest. rsync is easier to use than git, which is a million times easier to use than S3.
I might go so far as to say that storing compiled HTML on git is an antipattern, but that isn't to say that you can't mirror the generator and posts on GitHub.
Well, I would use git anyway because I want it to be under version control. I'm intimately familiar with git and I consider it no harder than rsync. There are so many benefits offered by version control that I wouldn't dream of doing it with something like rsync alone.