Too much weight on your hands coupled with the lack of more than 1 hand postion could lead to this.
Bar ends can give you a few extra hand positions (on the bar end, hand spread our spanning the bar and end grip area, hands on the corners of the bar ends, etc)
you may try to raise your stem if you can to put you more upright, or try a shorter stem if you have access to them.
I don't run into hand issues when I ride. I ride TT Base Bars and road drops which give more than a few hand positions. I also always wear gloves (mostly for sweaty hands and crash safety, moreso than vibration damping).