I know you say that the frame, etc. is the right size, but here's my concern with that statement...

I ride long distance on a bike with unpadded cloth handlebar tape, and I have no issues with my hands/wrists. Even when the frame is the right size for the standover height and the seat is adjusted properly for your pedal stroke, many shop techs don't pay enough attention to the overall "cockpit" length when fitting someone to a bike.
If you're leaning too far forward, you'll put undue stress on your hands, wrists, arms and shoulders. Over short rides, you feel it in the hands and wrists. Over longer rides it translates to shoulder, neck and back pain. I have an easy test to see if your reach is too long:

- get into a regular riding position and remove your hands from the bars. If you're falling forward without the support of your arms, then your position is too far forward. You can remedy this with a shorter stem.

Another thing (along with ergo grips) which may eliminate pain in the hands a good pair of gloves to help absorb some of the road/trail vibrations. Also, consider a pair of bar ends to allow yourself more hand positions to alleviate stress on the wrists.