It's entirely possible that hand position isn't your problem, at all. It could be your arms and shoulders. If you are significantly overweight, you may be partially pinching off the blood supply to your arms and hands when riding in certain positions. The problem could be all the way up in your armpits, where the artery is closer to the surface. Try riding with your elbows bent, and slightly akimbo (I just won a bet!). See if that makes a difference. If so, I don't know the solution, except to lose some weight.

I always ride with gloves after seeing what happened to my brother when he went down and put his hands out to catch himself and ended up with gravel embedded in his hands.