Tom I empathize with you. I have the same injury (right shoulder rotator cuff tear)
Mine is almost 10 years old. I finally figured out it will not rehabilitate on its own. For some people just leaving it alone might do it, but not me. I started doing these exercises. I try to do them at least every other time i'm in the gym:
http://familydoctor.org/online/famdocen/home/healthy/physical/injuries/265.htmlI do exercises 2 and 3 with a band. I should do all four I just haven't gotten around to trying out the other two. I am already seeing results. Less pain during lifts. Less clicking/knocking sounds in the shoulder during movements. Greater feel of control during lifts. By the way a physician recently told me this and I'll paraphrase: "Do not do shoulder exercises.. only use tiny weights close to 1 lb for shoulder exercises and do them every day high reps. You should do this for almost a year and it should recover". I'm not planning on taking his advice i'm just gonna keep doing resistance band exercises and back off any lifts that make it feel bad or change the exercise.
As far as exercises these are the ones that never really jack up my shoulder any worse than it is as long as I maintain perfect form and control:
Cable Chest exercises - none of these hurt my shoulder as long as I don't pick a weight so high I can barely control it
Seated Bench Machine - I pyramid up on these with perfect form. I can go pretty heavy and it doesn't jack up my shoulder as long as I have perfect form including shoulders back a little and chest up and out.
Hammer Incline Press - Again, strict form. I stand up and pinch my shoulder blades together and sit down in the chair and let up a bit just to get in position good. This one never bothers my shoulder either
Knuckle pushups (I do these at the end of chest day 3 sets as many as I can do). They are not for everybody but I would argue if your wrists are strong enough these give you a great pump at the end of chest day. Could be overkill for some people who have already nuked their chest
I just stumbled across this video on strengthening the rotator cuff. Some people do a bunch of these before every lift to stretch out the cuff