OK, so an update, finally! Sorry it took so long, but I had hernia surgery and was down for recovery for about 4-5 weeks.
So, bottom line up front, thanks to everyone's input here, I'm very pleased now with the setup!
The changes I made were:
1) Put one more washer in the WD hitch and also added the anti-noise pads on the L-brackets, which might equal another half-washer of pre-load.
2) Upgraded the tires to load range D so I could run 65 PSI
3) Fixed the slop in the steering column
The primary fix I think was just continuing to add washers to add more pre-load to the WD setup. One of my biggest mistakes was thinking the number of washers/angle of the head would look anything like any other setup I've had with this hitch - if I'd gone into it with no preconceived notions of what I thought it should take, I would have just kept adjusting until it was right.
Three of the tires needed replacing before the big trip anyway, so that was a smart upgrade and probably also helped reduce the squirrly-ness.
Lastly, there was a tiny bit of play in the steering that I had initially just written off as being a vehicle with 80k miles on it, but it did really bug me. Play was less than 1/8", but still noticeable and annoying to me, so I found a lot of folks saying the intermediate steering shaft was the culprit. I got one of the re-designed ones for $60, but as I was installing it, I found that the bottom bearing on the upper part of the column assembly had slipped almost all the way out! Amazingly (for a 2015 model year) this is a known issue, and there's actually a TSB out on it - not sure how my '07 GMC managed to go 150,000+ miles without the steering column falling apart but a 2015 Suburban does. Anyway, I fixed that too, and it eliminated almost all of the play, which was also a huge help in making the towing way less work.
Thanks again to everyone who pitched in with suggestions!
