The good part is you can do it yourself without GitHub (which, after the downtime, could come into the equation quite easily):

  -- Remote machine, or SSH port forwarded machine --
    > adduser git (you either add pusher/puller's ssh pubkeys to its 
      authorized_hosts, or use a shared password)
    > su git
    > cd ~
    > git init --bare myproject.git

  -- Your local repo --
    > git remote add <name> git@aforementionedmachine:myproject.git 
    > git push <name>

Setting up a git repo for confidential pushing and pulling is quite easy.

Already had the repo up and running elsewhere, thanks. Just needed to do some non-git stuff on github (create a new repo on GH to push it to, add team members, and so on).

I've been doing private DVCS for years (mercurial) but this is my first project that's on git and I've been looking forward to the opportunity to host it on github and see what I've been missing.