I suggest installing interrupter brake levers, so you can ride on the tops of the bars while still having braking at your fingertips. That will move your hands rearward by several inches and could be all you need. The levers cost $30-40 and can be installed without even unwrapping the bars.
Also, try this: sit on the bike, hands on the bars in riding position, then lift your hands just an inch off the bars, while keeping your body in the same riding position. Are you straining to hold your body up in that position, without support from your hands? More core strength will help. Now, try pushing your butt all the way to the rear of the saddle, and try the same lift-hands-off thing. Is it easier or harder to hold your body up? People often find it is easier. Moving the butt rearward balances the torso forward. If that is the case for you, you could try adjusting your saddle rearward, just a very little bit at a time.
If you do want to change the bar position, tell the bike shop you want a stem that has positive rise, meaning it angles up. You can get it shorter as well. In fact, there are adjustable stems, that pivot up and down and lock in place. They look horrid but might be useful to try different positions.
Hi jyl,
Thanks for your recommendations. I really like your positive stem idea! These are really great tips. You raise an interesting issue with the interrupter brakes. I already have interrupter brakes and ride them almost exclusively in heavy city traffic. Because they are located close together, I am wondering if they are aggravating my shoulder problem. When I last had a fitting done, they put wider handlebars on the bike, which helped a bit.
Would moving the seat back increase knee strain?