I have read on this forum somewhere that downtube shifters instead of the STI will help since the rider is forced to move hands to shift.
On long rides 1000 km or above I also have numb hands that take usually 6 months to go away. I try to alternate riding without gloves and use two of even three pair of gloves for long distance. It helped but I still had the numbness. I use Campy shifters and still trying to figure out the fit of the handlebars.
As mentioned above by
79pmooney rotating the bars forward helps, but I never went extreme(maybe I should)- my drops are parallel to the ground. I think increasing the reach will lower the pressure on the hands, but put more stain on the upper back, so there must be a compromise somewhere. I am still working on it...too bad I have to do a very long ride at least 600 km + to see if it works.