If you want a similar solution to GH instead of just a bare Git installation, you could look into running your own GitLab instance. Their software is open source and freely available. Of course, that way you would have to trust your hoster unless you are running your own in-house server.
Branch protection is also available in the open source GitLab CE. We made git-annex an enterprise feature because it is one of the few things that came up more from larger organizations, smaller ones tend to use a shared Dropbox.
Anecdote: I am an independent game developer who views git-annex as unproven, but who would also love to get away from Perforce. However, Perforce is free for up to 20 users, and right now my side project has one other person working on it - $400 for a year of GitLab is a non-starter.
More generally, I am curious how many of the "larger organizations" to which you refer in this context (clients interested in git-annex) are in the games industry, and how seriously interested your company is in trying to cater to that industry's needs? (Lots of game engines enjoy built-in first class support for Perforce due to how established it is in that vertical.)
We're pretty comfortable with rebase before merge being part of EE only. Someone suggested making an option to select the type of merge you want (ff, no-ff, log, rebase or squash). If someone would submit a good implementation of that and reference this comment we can open source everything. Edit: removed the work probably to make this a firm promise.