You should be able to use hg-git. hg clone
edit ~/.hgrc and add : [extensions]
hgext.bookmarks =
hggit =
create a bookmark so you will have a master in git : hg bookmark -r default master
edit .hg/hgrc in the repository and add : [git]
intree = true
now you can create the git repository : hg gexport
and you can use the resulting directory as a git clone. pulling from mercurial would be : hg pull
hg gexport
and pushing to mercurial : hg gimport
hg push
(Yes, you need to use hg with this workflow but your hacking will be all in git)
Git interoperability with a Mercurial Repository - Stack Overflow