I have R700 shifters on one of my bikes. I'm not sure how different these are than standard Shimano shifters that have been shimmed, but I do find they make a significant difference in how close the levers are to the bar. I can probably dig up pictures for comparison if you are interested (of R700 shifters on Ritchey Biomax bars vs regular unshimmed Ultegra shifters on Ritchey Biomax Bars).

Narrower bars are nice if you have narrower shoulders (as I do, in fact), but they won't help your hand problems.

The shape of the drop can make a significant difference. Rounder, more traditional drops, counter-intuitively, often have a shorter reach to the shifters than modern ergo bars have.

What everyone has said about braking technique is right on (you want to be relying more on your front brake than your rear brake), but if you are noticiing significant differences you should also check the brake adjustments. Can you actually pull your rear brake lever closer to the bar before engaging the brake? If so, you need to tighten up the rear brake.