I had a 2016 1500 with 8hp70, 3.21 gears, and the 5.7 before my current truck. We started with a smaller camper to "try it out" and see if we would enjoy camping (Wildwood Xlite 230BHXL). We pulled it from New Hampshire to the four corners, and up/over Wolf Creek Pass, and back home and it did great! We really liked camping, especially since it was a vacation we could take our German Shepherd with us on, but the camper was fairly small and not enough windows for rainy New England stretches of weather.
My next trailer was a Coleman 2855BH, which was about 5700# dry and 7500 maxed out, but about 32' long. My truck was rated for 8050# IIRC with the 3.21 gears so I was nearly at max towing capacity when loaded with the family and dog. My rear axle was over by a couple hundred pounds and I was within a few hundred pounds of the GCWR of the truck. Interestingly, I found that the truck towed REALLY well at slower cruising speeds on back roads and non-interstates, at 35-50 mph. The truck did not like highway speeds as much, it had to work harder to maintain the speed and fight the added air resistance. Highway speeds for me was ideally 62-65 mph. Towing in Canada on the highway wasn't as bad because of the lower speed limits. I felt that the truck was being worked pretty hard and it saw 3000 rpms on many small hills and it hit 4500 a few times. I don't mind if the engine has to hit those rpms occasionally, but it just didn't feel like it did much for forward motion, it just made more noise when I hit 4000-4500 rpms.
Technically, 3.92 gears would have given me the ability to tow more weight, but within the parameters of what I needed it to do, like many families pulling a travel trailer, it didn't matter because the remaining capacities would be exceeded.
When I bought that truck I wanted 3.92 gears but they only had 3.92's in a black tradesman, which was okay, but the Big Horn with 3.21 I ended up with felt identical on the test drive (not towing of course) and was much better equipped. I reviewed data while considering swapping axles to 3.92 gearing but ultimately decided there wasn't going to be enough of a difference to justify the cost, especially with the limited payload, axle ratings, and GCWR. I read many times that the 3.92 geared truck was essentially one gear higher than a 3.21 geared truck once the load was moving. My conclusion was that I would be far better served with a 2500 and 6.4 with 8hp75 as that would check all the boxes that the 1500 was unable to, and no matter what, the gearing wasn't changing the gcwr or axle ratings.
Both trucks had a leveling kit; the 1500 was 2.1" and the 2500 is 2.5". Both trucks were running about .75" upsized all terrain, severe weather rated tires on aluminum wheels.
*Payload- doubled from 1500# to 3100# - and this is usually the limiting factor when towing campers.
*Towing- 8050 to 14,410#
*Towing mpg were very close but the 6.4 showed about .5 mpg better with the same camper on the same routes.
*The 6.4 cruises along at about 1800 rpm on flats, jumps to about 2100 on smaller inclines, and hits 3000 rpm on long stretches of 3-4% grades. The 6.4 is overall a much nicer towing engine.
I decided I was finally going to try a 5w since I had a 2500 and I got a Cougar 30RLS, which has a gvwr of 11,000 vs my Coleman 7,500. I get slightly better mpg towing the 5w and it's easier to tow than the Coleman tt. The best decision I made was moving to a 2500 and 5w.
In my opinion, the 3.21 vs 3.92 gearing isn't going to be as significant a difference as the OP wants, which was the same for me. Upgrade the truck. The 2500 rides about the same as my 1500 did on e-rated tires. I run 17" wheels in the summer and 18" in the winter. When my 1500 was stock I could get 19-20 mpg on the highway, but leveled and with the 34's it got about 17 mpg highway. My 2500 gets 16-17 highway with 34's. Cruising around town is about 15-16 in the 2500 and 17-18 in the 1500. The 2500 needs an airfield to do a U-turn whereas the 1500 was more maneuverable.
My insurance DROPPED going from the 2016 1500 to the 2019 2500.