Try Alwyn Cosgrove's half of the "8 Weeks to Monster Shoulders" program he and Chad Waterbury put out a few months back. I had much the same problem as you in that I had a nagging pain in my left cuff that would not go away and kept me from any serious overhead pressing for some time.
In fact, there's nothing wrong with adopting the whole program, I just needed Alwyn's half and I was good to go.
Also, is your pulling volume equal to or even greater than your pushing? That was also a problem with me and since I have corrected that I've had no pain in my shoulders and am now back to chasing a bodyweight o. press.
Also, Eric Cressey has the Neanderthal No More articles with Mike Robertson and Cracking the Rotator Cuff Cunundrum which are awesome resources for working on mobility, prehabilitation and imbalance correction all of which probably apply. All of those can be found via the search engine here. Good luck, hope it helps.