There's a few things you can try.
There are gel tapes around that are a bit more padded.
You can get gel inserts to put under your tape (or fashion your own out of old inner tubes)
You could try double-wrapping the bars with more tape.
If you keep getting pins and needles though, I'd be checking the bike set up though. I'd suspect your bars are a bit low and you are putting too much weight on your hands/wrists.
edit - x-post with the blue guy