Lots and lots of speculation here.
OP....can you clairify what year F150 you have, what motor, cab, drive, and axle ratio do you have. Also, can you provide info on your brake control.
What about your WD hitch with either dual friction sway controls or integrated sway controls.
I pulled a "gasp" 31 ft TT with a F150 all over Tennessee and never once felt unsafe or out of control. I actually felt comfortable and enjoyed the ride. The brake controller was properly set up and the WD hitch was ideally set up for my truck. I used dual friction sway control as as well.
The answer to some towing problems may be something simple....tires, hitch, worn parts.... So many get the "gottahaveits" and just buy a bigger truck, replacing a perfectly good and capable truck. Which is fine.
Thanks!
Jeremiah