This may be as simple as how your wrists are located on the current grips. The top of your arm should be essentially parallel to the back of your hand, with very little bend in the wrist. If you are bending your wrist to rest on the grips, rotate your bar or grips so that everything is supported in line.
Ergon grips are far superior to the stock Specialized grips, regardless of the "body geometry" title on them. The short bar end Ergon's do not put your far from the brakes, and are so easy to adjust for perfect fit.
Raising handle bars (ie adjustable stem) is not necessarily a plus for wrist / hand pain. If you are riding with all your weight on your saddle, and little weight on your hands, then vibration can cause pain. Ideal weight distribution, IMO, is 50% on the pedals, 40% on the seat, 10% on your hands. Sometimes lowering your bars gets you to that distribution easier than raising the bars does.
It is unlikely that you can get a short enough stem to actually get drop bars comfortable, especially if you are averse to a long and low position on the bike. If you are at a 90mm stem now, you would need to go to a MTB stem to get short enough.