Since going to a more aggressive posture there are two areas where I'm feeling some discomfort.
The palms of my hands and my shoulders.
I've been doing core work at the gym to decrease reliance on my hands and shoulders, and there has been some success,
most notably in the shoulder area. But my palms still get a little achy.
I replaced the stock grips with Ergon grips and there was a marked increase in comfort.
I'm currently using good quality, gel gloves, the Pearl Izumi gel vent's.
Excellent gloves, but I would like some additional padding in the palm.
Any ideas?

How long into your ride before your palms get sore?

Having the exact same problem, and most have told me I'm just not fitted properly to my bike. That it's in the seat positioning. I'm currently researching who to do this for me to get results without wasting my money.

I angled the Ergon grips downward (so there was less pressure on the palms) more than you'd expect, and it actually helped a bunch. I also bought these gloves and it help a bit more: Amazon.com : Louis Garneau 12c Air Gel Gloves - Men's : Sports & Outdoors

Excellent suggestions. I just now lowered the angle of my grips and I'll give you some feedback after my next ride. The gloves look very promising. Thank you.
I"m curious as to seat position. What adjustment did most people suspect was needed?

Primarily, the fore and aft. Maybe tilt also.

I'm also looking for a super well gel padded fingerless glove, but am frustrated by reading the negative Amazon reviews on most of them. Pretty large percentages complain of lack of padding and poor stitching on the most common and readily available brands. I'll name names: Pearl Izumi, Louis Garneau, Giro. Seems like all are lacking- what other brands to consider? I'm interested in quality, durability and feel more than price.

You can try weight lifting pads like this one
Amazon.com : NewGrip Power Pads l Gloves for Weight Lifting, CrossFit, & Pull-Ups (Medium (5'4"-5'9")) : Sports & Outdoors

I added these under my bar tape to add a little cushioning and it really helps for those times you rest more weight on the bars. Core strength is key, as you stated, to keep weight off the bars!

https://www.amazon.com/gp/product/B00...g-goods&sr=1-2

I like the Performance Bike Crochet Gloves.

GH

I picked up a pair of Giro Strade Dure Supergel gloves about 3 weeks ago, and so far, they are absolutely fantastic. I was previously using the Ironman Rip-It padded gloves. They were quite good for a number of months, but the gel pads began to break down, and once the large pad below the thumb flattened out, they became just plain uncomfortable. Far too soon to say on the Giros, but they were definitely better right out of the package than the Rip-Its.

I don't have the strongest core in the world, so once a little fatigue starts to set in I find myself supporting more weight on my hands than I probably should be-- and the Giros have improved the late-miles comfort dramatically. With the longevity still unknown, they're comfortable enough that I would recommend them-- if I manage to get 4+ months (~3,000 miles) out of this set, these will be my next pair, and the pair after that.