More stuff: I ordered the door sag kit for the driver's side, and figured I might as well do the passenger side while I'm at it. Also ordered a spring compressor tool and a spring, as the driver's side spring is missing.
I also suspected that I didn't have the weight distribution hitch set properly, as it was putting too much weight on the rear wheels, which made the front end (and steering) a bit light. I think that might be contributing to sway when trucks were passing us. So I contacted a local RV dealer (Bish's RV), intending to tow the camper there and have them set up the hitch properly. Instead, they had their techs call me up and do a video conference so they could see my setup. Didn't cost anything, and it didn't take long for the tech to explain what I needed to do, and why. Now I understand what I'm doing, and won't need to take it to them to have them set it up. Glad I called Bish's!
Our next trip is in a couple of weeks, so I'll hook it up the day before departure, using my new found knowledge.
I also decided to become a supporting member. This forum has already given me value well beyond the price of admission. I plan on having the '96 Suburban for a very long time, so it was an easy decision. Plus I have a '93, which will be needing some TLC.