FWIW I had a very long discussion with the technician that replaced my tranny. He said it is "happiest" towing my 7000 boat from 220-230*. But it will start pukeing transmission fluid at 240*. The radiator and tranny cooler are somehow connected and the transmission and engine temps should usually be within a few degrees of each other. My photo shows that isn't always the case.
The only reason I'll continue to occasionally pull my Malibu in the mountains with the Ex is because I bought an extended warranty (first time I've done that with a car). With the prices of new transmissions I wouldn't do it otherwise.
Sharing my opinion because you asked, I think you are asking a lot of your truck to do what you're proposing. And my experience is that tow can be very detrimental to your truck. If you plan on keeping it, I'd look at other options. A friend with a HD. Rent a truck from U-Haul or Enterprise Trucks for the day.
Good luck however you decide.
As an aside, that houseboat reminds me of the first one I ever was on. It was about 1980, my folks "borrowed" it from a friend. My cousin was driving it, following two pontoon rentals. They went between and island and the canyon wall, and he followed. We quickly found out that a stern drive draws more water than a rental pontoon, and we hit ground.
Most memorable was that the owner of the boat somehow ended up coming out to help us and dove underwater to change the prop. My memory had him under water for something like 5 minutes at a time with a mask and a wrench. I'm sure that it wasn't that long, but it was impressive. And he got us back on our vacation.
Pretty sure that boat was a Gibson. But they seem similar.