Asking for a recommendation letter from an open source repository mentor
Go for it. 

I had the doubts like you earlier. But changed my mind after talking to one of my mentors. He fits all your above descriptions. He said, he would be happy to give a recommendation letter to his Google Summer of Code (a remote open source summer internship sponsored by Google) students who performed exceptionally.

While you do not have a student-professor relationship, he might be the only professor that ever witnessed you coding in a professional environment. He might have noticed your positive sides that other professors will never have the chance to find (except on academic projects).

Just ask. It won't hurt. If the professor feels he does not know you enough, he will let you know.