After 8 pages, no one has even questioned the weight on your camper. A 24ft Rockwood for under 3K lbs?
I have a 2014 Flagstaff High Wall 14" pop-up that weighs more than that.
Anyway, I have a 2013 F-150 5.0. If the terrain is flat, I'm not bucking a headwind, and I keep the speed in the 6o-65ish range, I can tow in 6th....but I've only got about 32 sqft of camper frontal space and the only thing that sits higher than the cab of the truck is the camper A/C unit.
HOWEVER...one I start getting into the mountains or hilly terrain, that's were things start to change. A non-turbocharged engine will loose roughly 3percent power for every 1000 feet. Depending on where you're at, you could be loosing in excess of 25-30 percent of the power. You could easily be loosing upwards of 75 HP or more, which also effects torque, which ultimately effects towing. And these #'s don'e even include the paracitic power loss by having a 4x4 truck and having to route power thru a transfer case.
The BOTTOM LINE is that all pickups are designed to maximize fuel economy. This is done with transmission shift points, engine power and fuel management computer protocols.
The manufacturers give you the option of overriding the power/fuel management protocols by such things as tow/haul mode, being able to lock out certain high gears and other things. Basically, you have to be smarter than what you're working with. A pickup hooked up to a trailer will do everything within it's computer programming to deliver the best MPG available.
I'm personally willing to lock out higher gears and let the engine run at higher RPM's instead of letting the transmission hunt, and hunt, and hunt to try to find the highest MPG. You can do whatever you want, despite all the sound advise offered, but I personally don't have over $3K-5K for a new transmission...maybe you do.