I have a nagging shoulder problem as well, as I have dislocated in several times through the years. My doctor told me that short of surgery, working out to build the muscle up around the joint would be the only thing I could do. If you build muscle mass around it, it should help stabilize the shoulder. But if have worked out a lot, you might have injured your shoulder and didn't realize it. Could be just stretched ligaments or they could be torn. By the way, I use stock DK Opsis bars, and I'm right at 200lbs and 6'02"...and they feel good to me. I don't think it's a set up problem.Just do some light stretches before you ride. Do over exert your ligaments/tendons though.
The advice you'll get here on how to deal with your bum shoulder is probably as good as the flatlanding advice you'd get from a board for physiotherapists. Seriously- talk to someone who knows what they heck they're doing and you'll get an answer you can actually rely on.