In my experience, a couple of things were going on.

First, I found that I was using a "death grip" on my handlebars, for no good reason. I had to consciously relax my grip.

That helped some. Another thing I noticed was that if I was particularly tired, I tended to rest more of my weight on my hands. I had to make an effort to just sit up a bit straighter, and not lean down so hard.

Of course, there's the changing your hand position solution, except with straight handlebars, there aren't many choices! :-)

I'm also a big believer in gloves, especially padded ones. I did a test ride just last night w/out the gloves, and really noticed a difference.

One caveat regarding gloves: make sure they fit! I first had a pair that was too small, and if anything, they contributed to the numbing!

Good luck!