I pinched that nerve by cycling, and temporarily lost function in one of my hands - couldn't spread my fingers apart. My doctor, who is a cyclist, and I figured out the injury occured when I was riding in my drops. So he put in in a wrist brace, then sent me and my bike to his favorite LBS for a professional fit, where pretty much everything Kiwi Stoker described happened - the fit, moved the handle bars, corked bar tape, new gloves.

New bike added the carbon fork - and I made sure it had the corked bar tape. I haven't reinjured myself either in 5 years. I maybe be slow on the uptake sometimes, but I do learn! And I really don't want to ride another season wearing a wrist brace, that was no fun.

Writing this reminds me, I need new gloves....

So my 2 cents is - make sure you've had a professional fit, and tell the person doing your fit that you're having problems with your arms / hands, that way they look at your reach and not just what your knees are doing.

Good luck, and I hope your hands start cooperating soon!