My gloves are not padded however as I was riding home today I noticed that the padding on my handlebars is pretty much non-existent so I will look into some touring/gel setups. I also think my handle bars are too narrow, I was noticing that my wrists were a little too bent and when I moved them out to the extreme edges of the hoods it felt better.

The idea of one arm longer than the other sounds interesting, I'll measure just in case. The idea that the right hand doesn't cramp because it's shifting etc also makes sense.

I did try the 'piano' grips which helped a bit but more I think because I was moving my hands around.