As a body builder with a history of shoulder injuries, this is oversimplifying at best and wrong at worst.

You yourself recommend band work which is putting your shoulder under load

The real answer is the shoulder is complicated mechanically and you need to work on reinforcing or building the smaller groups (Is, Ys and Ts type of exercises and many others), if you can actively stabilize your shoulder this way you will reduce pain, inflammation and decrease the propensity for injury, allowing you to do traditional shoulder exercises like press etc without issue. I suggest working with a good PT