Too much TT for the truck. I have towed my fair share of I5 and mtn roads in Oregon. Had the same exact sway issues you're having when I towed a 31' 7300lb loaded TT with a 2010 F150 145" WB. Out on I5 you're susceptible to winds and semis because it's more open. In the mtns the TT is forced laterally into curves so it feels more solid. Plus there's usually not much wind blowing or semi's to pass. It was always that way. Great in the mtns, horrible on the freeways.
I traded that truck for my current 12 Ram 2500. Way, way better towing experience. Even thought the TT still waggled a bit, the 2500 stayed solid and wouldn't let the TT move it around. I was using the EQ with 4pt sway control with the F150. I had plenty of tongue weight at 900-950lbs. In comparison I towed the TT with both trucks and only used an EAZ-Lift with the Ram 2500. It towed better like that than the F150 did with the EQ.
I even had E rated tires and SuperSprings on the F150. It just boils down to physics. The F150 isn't enough truck for 8000+lbs and 33' IMO.