Maybe I'm the only one who doesn't think you're in a bind here. Now if you're not used to towing ATs a lot of trailer for any truck and yours in particular. If you're towing thousands of miles a year, it prolly too much trailer for a 150, just from a comfort while driving standpoint.
But the frames, axles and brakes on the newer F150s are pretty stout and you got as much power as you can get out of any stock gasser for the most part.
I think you're fine with a wdh on it and good tires on the truck.
Would I have chosen a smaller trailer or HD pickup, ideally yes, but you're not off base with your combo.
He!! The Tundra can tow the space shuttle. You just got a 30' camper! Lol