I've had the same trailer with the same EAZ lift weight distribution hitch and 2 friction type anti-sway bars for 20 years spanning 3 different vehicles around the country with somewhere between 50 and 70k miles traveled. My trailer is a 27' 7k GCVW and typically I tow with it loaded at about 6-6.2K. I think there are many good points from others here. I've had issues setting up all 3 vehicles for stability, a 2002 1500 Chevy Express Van, a 2011 1500 Chevy Silverado, and my current 2019 1500 Ram. Getting the tongue weight right and the correct truck squat takes alot messing around to get hitch set-up correctly. I do use the wheel well measurement method, but I also use a truck scale to verify setup to make sure I'm not over-loading an axle or GCWR.
I had similar concerns with the swaying when I got my Ram, it seemed a little squirrely much above 60mph. I think part of my issue was worn leaf spring bushings on my trailer, they are plastic and last less than 5k miles. I was told that wasn't the issue by someone that I would consider an expert, but I'm still think it may have been some part of the problem. I added the Hellwig solid rear sway bar, since I used that on my last 2 vehicles, not sure how much that helped. I think one of the bigger problems I have is the 275/55 R20 SUV tires, they only have a max pressure of 44 psi. I first started at the posted pressure on the door sticker, obviously that was too low. Tires should be a LT tire at minimum for towing, with higher ply equivalent side wall to stiffen things up. Problem for me is I want an all-season tire, not all-terrain tire since I don't 4-wheel offroad or want the added tire noise.
I just took my trailer to Yellowstone from Chicago area (~3k mi round trip) with the OEM tires pressured up to 44 pounds. Also before I left replaced all of the worn out leaf spring bushings, and replaced the trailer tires with a higher rated sidewall ply to jack the max pressure up to 65 psi, from the original 50 psi tires. This seemed to be ok when there weren't any cross winds. I cruised at about 70mph alot of the way hitting 80 when passing for short spurts, but when I hit windy conditions, dropped back to 60 mph sometimes when the trailer started getting a little squirely. I will be due for new tires next spring, and I will find some stiffer wall tires, but don't want 8 ply equivalent for ride smoothness when not pulling trailer.
As far as towing 6 or 7k trailers with a 3.21 gear, I don't have any problems with that. I only trailer 2 -4 weeks a year, and I want the better ride and mileage for when I'm not trailering. The 5.7l engine has way more HP than either of my other tow vehicles I had. The biggest difference is the transmissions, I went from a 4 spd in the Express with a 4.1 rear gear, to a 6 spd in the Silverado with a 3.42 gear, to an 8 spd in the Ram with the 3.21. Yes, the engine revs more with a trailer and may not get into 7th or 8th depending on grade. I had some steep grades that on rare occasion stepped down 4th or 5th depending on the speed you're trying to maintain, but these engines can handle that, it's not an issue of power.
I logged my gas mileage on my Yellowstone trip, checking the truck computer reading with actual pumped gas vs miles, they matched fairly close for 3 or 4 tank full's, so I just started using truck readings. The lowest I got was about 7.5 mpg in the mountains. At first I was using mid grade gas that had ethanol because that's all you can get in most of the midwest. When I started using gas with no ethanol and started using premium, my gas mileage was much better. Driving home from Yellowstone, using non ethanol premium, the lowest mileage was about 9.5 mpg. Part of this was I think it was more down hill than when going there and maybe less windy days.
My opinion on towing and what truck/gearing to use is mostly about how the truck is used over the year.
My Ram for what I need works perfectly. If I had a truck for a business and towed frequently, I probably would opt for a 2500 with a bigger engine and rear gear. Anything in between is going to vary based personal experience, budget, and comfort zone. Personally, I think pulling a 24', 4k trailer on weekends shouldn't be an issue for Ram 5.7 with a 3.21 gear, just have to get past the gear selection, higher rpm's and lower gas mileage when towing.
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