Hi, Chris. Thanks for your question I took it to an orthopedic surgeon, Dave Jacofsky of the Mayo Clinic, who happens to move a fair amount of iron himself. He suggests doing exercises that isolate your chest, instead of utilizing chest and shoulders in tandem. The more inclined the bench, the greater the stress on your shoulders, so you’re better off doing less military press and more cable crossovers and flies. These engage chest muscles, but don’t involve heavier weights and are thus easier on your shoulder.
Other suggestions include getting to a sports medicine clinic for some PT to rehab the rotator cuff. They may help you strengthen it enough to get you back in the game a little more. As for the bench-press question, the bottom part of the exercise does put extra stress on the anterior deltoid. Bringing your hands a few inches closer together on the bar will help by putting more emphasis on the central portion of the lift, where the chest and triceps do the heavy work.
And here’s my piece: perhaps you can use this as an opportunity to get away from a big weight/big muscles/barbell-oriented workout, toward a routine that focuses on greater functionality, using dumbbells and balance work. Chances are there are holes in your repertoire of basic movements (push-pull, step-squat, rotating and side-to-side) that you could spend many less-muscle-stressing workout hours fixing. You’d also stay buff, because your body would have to radically adjust to the novelty of it all.