I should have also mentioned that the guy at the bike shop didn't think that gloves with too much padding was a very good idea. I got the Bontrager Solstice gloves that aren't too padded and they helped.

He verified the fit of my new bike, so that's good to go.

He also said I could consider more ergonomic grips if the problem persists.

I guess the bottom line is that I need to strengthen my core (e.g. lose the extra weight I now carry on my upper torso, lol) and then see if that helps resolve the issue.