Any access to different style grip bars? I find for some a more neutral (hands facing each other) grip may alleviate this and allow for continued pressing activity. If no bars allow for this have you tried DBs with varying hand positions?
You could try a bunch of different angles as well. I've found for various reasons one angle sucks, but another feels fine, so find what feels ok for you. A very slight angle always works best for me (even as low as like the bench is flat but I put a plate under one end).
Maybe try some weighted push ups (of varying angles as well). Load them up with weight vest or do on things like straps/rings for increased difficulty. Sometimes activities like that where the back isn't in contact with something like a bench can free things up and work for some.
Shoulder pain sucks, hope you can get some other good suggestions in here as well. Maybe check out some things to try and help the underlying issue as well. Good luck!
BB or DB pullovers. Make sure to not go back/down too far where you would engage your lats. Ive had some shoulder issues the past year as well. Standing bench with bands were pretty pain free. This kind of goes along with what Resolve said.