Another older thread by now, but the issue is still timely, so...
Have you considered raising the handlebars so the tops are near-equal in height to the saddle-top? Back angle can be restored by bending one's elbows, which further aids in shock absorption. I've found doing so reduces the amount of weight carried on my hands, and is a lot less painful over long 400km day rides, even when those rides include long stretches of gravel and rough asphalt. You might need a taller quill on your stem (if it is of that type) or a threadless stem with greater angle to accomplish this. Randonneur-bend handlebars (they look a bit like gull wings when viewed from the front...they wing up from center to the brake hoods, then flare out at the drops) can gain you between 1cm and 1.5cm in height alone compared to a Maes bend.
I have recently considered adding some under-tape gel pads to my drop handlebars. Bontrager and Fizik are two brands I've seen and considered, and they are available as pads or in sets that include pads and tape, which may be gel-padded as well (ideal for the cobbles of Belgium...they were rougher than I'd imagined). I use gel-filled cycling gloves (prefer Pearl Izumi brand myself), but recently experimented with placing a gel forefoot shoe insole between my gloved hand and the tops of the 'bars, just behind the brake lever hoods. Bliss! Worth following up, methinks, and I plan to when I next replace my bar tape.
As a further data point, I've found tires with larger profile height and section width are helpful, and allow for running at lower tire pressures. Tires provide a remarkable amount of suspension and surely ease the pounding one's hands would otherwise suffer. There is growing evidence that when the road surface is poor larger, softer tires may be nearly as fast and efficient as narrower ones run at higher pressures. I know I am as fast on my randonneur bike with 32mm tires run at 85 psi as I was with 22mm tires filled to 125psi to prevent pinch flats. Your experience may differ, of course.
Hope this helps someone,
Dan.