Thanks for all your help! I don't think the problem is with the saddle, I've spent a lot of time working on that, proper height and fore/aft position, etc. I can ride for an hour and not get uncomfortable or slide around on it.
After some tinkering this evening I think the problem may have been in the angle of the handlebars. When I flipped the stem to get them lower I must not have paid much attention to the way they were rotated inside the stem. I rotated them maybe 10* inside the stem, and bam, problem seems to be gone, and I didn't have to raise my handlebars

Seems like they were pointed down a bit and it was causing me to carry the weight on the meat between my thumb and index finger a bit too much. Now it feels more even on my palm.
I'll update this thread if I go on a longer ride and its not fixed.