Experiment with lifting the nose of the saddle a touch to tip a little more weight back off your hands. Research 'ulna nerve'. If your weight is pressing that you will experience similar symptoms and pain. Try rotating your bars up slightly, or raising bar height with spacer configuration. You're aiming for a neutral (weight) distribution between your butt and your hands. Even less on your hands if you can find it.
Failing that try gel pads under your bar tape, even self adhesive neoprene under the tape.
In short, experiment until you crack that sweet spot.