To answer your questions....
the GVWR of the 5'er is 14k
X 20% = 2800 lbs.
I was sort of planning on the f350, but since you brought it up, would the f250 be sufficient with air bags added ? I know there isn't a lot of difference in ride quality anymore, but if the 250 would work, I'd rather go for that. It would be a couple inches lower.
Then I read an article like this and it might as well be written in Chinese.
Caution – Why Truck Tow Ratings don