I feel you should have some horizontal pulling in there for you rhomboids to help with posture so my suggestion is:
1) 50 pull-ups (or variations)
2) 50 inverted rows (or variations)
3) Spend 10 minutes working on progressions towards a new bodyweight exercise. Front levers are cool, and a nice skill to have.
I do agree with AG though, a bodyweight only back workout is probably not your best bet right now. I think you need to think about the "why" more. As in "why do I want to do only bodyweight exercises for my back", "why do I feel I need more varied exercises in my program" etc. Imagine your lifting hero was going to come and ask you these questions at your next training session.