I have NEVER had any relapses as I stopped pressing except for just STRICT dumb-bell presses, I do those and laterals- and rope pulls at eye level for rear delts...
I've done them too (face pulls, bent over laterals) with good success. Another thing I noticed (I had bad bursitis/impingement) with the shoulder pain, and this actually held back my recovery for some time. Side laterals didn't 'hurt' to actually perform, so I kept doing them, albeit with fairly light weight and higher reps, but they seemed to actually exacerbate the problem as a knock on effect. I don't do them any more and it was only after eliminating them as an exercise that the pain/mobility issues went away. So whatever work the medial delts get it's from regular dumbell shoulder presses, and they haven't suffered (I'm no threat of getting an ifbb pro card mind you). Apart from that I also do said presses with palms facing each other, or nearly so, rather than facing forward, seems to have been another piece of the puzzle.
I've been able to resume barbell bench press without pain too. One thing I did change was more thorough warmups, including an initial 50 reps with just the empty bar. It doesn't 'feel' like it does much at the time you are doing them, but has made a difference longer term.
A lot of people have gotten some relief doing the shoulder stretching with a broomstick (dante/dogcrapp talked about this years ago on other forums, it's out there if you google it), but for whatever reason, they did nothing beneficial for me, and I don't do them now. But worth a look as I'm definintely in a minority there.