I haven't read all the numerous responses, so much of this may be redundant. Just my two pennies.
I have a 2020 Big Horn quad cab, 5.7 hemi, no e-torque. When I bought it, the salesman knew I would be hauling a trailer. The one I demoed had 3.92, the one he sold me had 3.21. I was very unhappy, but neither the dealership nor RAM would help me out. I have a neighbor who also had a RAM 1500, 2017, 5.7 hemi, 3.92 gears. His had a 12,000 # towing capacity vs. my 8,000#. From what he has told me, he got around the same mileage I am getting when towing, so I am not all that concerned. The 8 speed transmission really compensates a lot for the gear ratio of the rear end. As far as engine RPM goes, think about it. The final drive is a combination of transmission and rear end. That ratio changes as the gear changes regardless of rear axle ratio, they just aren't at the same points. In any event, the engine needs to stay at a certain RPM to develop the needed power, regardless of gear. My camper is 4,400# dry weight. I'm usually around 5,200 fully loaded. My goal was to stay under 75% of the towing rating in order to have some headroom for hill climbing, passing, etc. I am hauling less weight than you and my tranny is generally in 6th, occasionally into 7th and eighth. On a trip from VT to FL, it went into eighth gear a total of 4 times, always downhill. I always use tow/haul when towing, it just makes sense. All it does is change the shift points, which is easier on the engine and tranny. Without it, there is far more up/down shifting. I've tried it both ways and I don't see any positive effect on MPG, so why beat the truck? The comment about having your loaded rig weighed is a good one, especially for WDH setup. Most people don't do it, but it can have an effect on gas mileage, and even more important, handling. Anyway, for the math. You have to keep in mind that the payload is a combination of many things, including fluids. My RAM has a 26 gallon tank, so I am hauling 156# of fuel. Add to that occupant weight of 400#, gear in the cab at 100#, trailer hitch at ~60# (e2 WDH), gear in the bed at 4300# and minimum recommended 10% tongue weight of 520# and you already exceed the 1,500 payload by 36#. It's really hard when towing to stay that low and I do it by shifting as much as I can to the trailer, rather than hauling stuff in the bed. Each 100# moved from the bed to the camper reduces payload by 90#. Not bad. If you're more toward the max capacity of tongue weight at 15% it's even more important. On my next trip I plan to move even more to the trailer, since it has a 1,500 pound payload capacity which means even loaded to capacity, it only consumes 150# of the truck's payload capacity. I also have heard that the trailer will handle better, but we'll see.