Though what I am about to tell you will be frowned apon by the cycle fashion "must-look-cool-at-all-costs" police, it has proved to be the solution to hand numbness and tingling for me.
I put the Ergon GP1 grips on which helped somewhat but as my rides got longer the problem was still there. I googled bar ends and didn't really like the idea of my hand way out there away from all controls plus I have a mirror sticking out of one side which would have required a rethink.
Then I found a couple of designs of bar "ends" that go inboard of the grips. Being some what lousy I was loathe to part with another $60 bucks for another experiment that may not work so I went to Ebay and got a pair of $15 cheapies. Having small hands, I noticed that there was about half an inch of grip on the inner end that I never used so I trimmed that off and the bar "ends" fitted with just a little tweaking of the brake levers and gear shifters.
I can apply gentle (but not panic "Oh ****") braking with my pinky and adjacent (what is the right name for that finger) finger and change the rear gears and so retain some control without having to move my hands. I never change the Front gears cos it is so flat where I live. I had found that resting my hands on top of the brake levers when the numbness kicked in did help but I felt I had not enough grip whereas now I have something that I am holding on to and the move back to the main grips is very quick.