Have you tried hg-git? I've been using it as my sole way of interacting (well, other than the web interface) with GitHub and I haven't run into any showstoppers.
I also use hg-git almost exclusively. My main issue with it is that pushing and pulling takes considerably more time, from 20-30 seconds for plain linear commits up to many minutes if there are merges involved. It's not a showstopper for me (especially considering the alternative of working with git direcrly) but I can see it being more problematic for people that tend to push on every commit.
My workaround is to also keep a local git mirror (git clone --mirror) and push through it:
Note that the installation instructions on that site are completely out of date. You don't need a C compiler anymore, just clone the repo and enable the extension, as described in the README: https://bitbucket.org/durin42/hg-git