JJ805, I agree the motor is the limiting factor. I pulled 6k with an 03' Expedition with the 5.4L 16V and 350 lb/ft of torque. Your 05' has the same displacement of 5.4L, but 24v and 365 lb/ft of torque. The Expo did great on hills but honestly it wasn't as stable a towing platform as the Sequoia. And the Expo transmission was junk at 103k miles. I think it may be the rear IFS in the Expedition which makes it much more squirrely. On the flats I would take a Sequoia over an Expo every time. But not at altitude.
I pulled around 4k (loaded) with the Sequoia for many years and didn't have power issues. I just stepped that up to about 5200k (loaded) and pulled steep long grades in the Rockies, the Sierras and Tushar range in Utah, often going to ~11,000 feet. The power concerns are real. The motor will pull it, but it will also get hot. The needle on the dash never got close to overheating, but the scanguage doesn't lie. The transmission never skipped a beat, but as motor temps rise the transmission has a harder time keeping cool. If I had an unmaintained vehicle, or earlier model year with less power, or pulled more weight then I could see the motor having issues.
Right now my plan is to go 70/30 mix in the radiator and keep it maintained to a fault. She's got 139k on her so a new radiator might be in order. The thermostat and water pump are fine. A larger transmission cooler may also be in order. As for increasing torque I am open to ideas, I haven't found any reliable cost effective solutions. Ultimately there may be no replacement for displacement.