Some years ago I did something to my upper back and/or neck area when doing a pullup and haven't been the same since. At one point about a year ago, if I extended my right arm my right hand went numb. That faded with time, but still, if I sleep on my side and extend my right arm too far, the hand gets numb. So that brings up the question for you to study, are there any other circumstances where you get a numb hand? Driving with your hands up on the steering wheel for a long time? Lying on your side with an arm extended? Maybe the problem is not pressure on the hand from the handlebars, but elsewhere, and it just shows up because when you are on a bicycle you are in just the right position for it to happen.
Of course I have no solution. I do try to make myself do some yoga postures just to keep myself from getting solidified. That seems to help, as indicated by the phenomenon that I get worse when I slack off.