I noticed that git branches are well imported and then re-exported using hg-git, but in the form of bookmarks. This may not be very convenient for you, but you can try the following:
- git first clone the existing github repository,
- then create a new branch (git), then commit and click,
- finally clone github repo to hg using hg-git
After these steps, you will see a new git branch in hg (in the bookmarks list). You can work on it in a classic way: hg update -C <name>then commit. And when you click on the changeset related to this tab, hg-git should add a new changeset to the corresponding git branch on github.
I know this is a little cumbersome .. but it can help you nonetheless.
Cheers,
Christoph.