(I don't use that rsync service so I'm just guessing as to how you use it. If you can provide more context, I might be able to help further.)
At the moment, the feature set around git workflows is not more than just providing authorized access for several users to a git repo itself but I'll be providing more features around this soon in a way that improves on what currently exists on git hosts.
If multiple people need push access to a private repository, just serve a central repository as on a VPS and use SSH for authentication. I am not sure if there is a reason to use a third party hosting service for this, especially when hosting private repos.
[1]: https://git-scm.com/book/en/v2/Git-on-the-Server-Getting-Git...
Reminds me of this comment https://news.ycombinator.com/item?id=9224
Edit: I don't mean to dismiss your comment. I just mean to say I'm obviously comfortable doing what you described but it's not a trivial amount of effort even if it is conceptually straightforward.