I was in the same boat as you are. 2010 F150 XLT 4x4 Screw 5.5 bed 7650lb GVW MaxTow. 1857lb payload. I put E rated tires on, SuperSprings and used a 1200/12,000 EQ 4pt sway. TT weighed 7300lbs @31' OAL. Truck and trailer were fairly stable. Light winds would move it around. Passing semi's on the freeway would give the usual push pull affect. Truck was maxed on RAWR and GVW. No matter whether I ran the E tires at 45 or 65 PSI. It never really made all that much difference.
It's just a matter of physics. There's a lot of surface on an 8'x26' wall. Add in the lighter F150 and no matter what you do you can't change the physical nature of the combo. Never had a white knuckle experience. But I always felt the TT back there and knew I was close to the edge at times. As long as the conditions were good then towing was fine. But once a light breeze came up then I had to pay more attention to the TT.
I traded the F150 in on a 12 Ram 2500 4x4 CC LB CTD. That's where the biggest improvement was noticed. Even though I could see the TT waggling, it didn't move the 2500 around. Where I would feel the need to have two hands on the wheel was reduced to a relaxing one hand drive. We traveled the same roads with both and one section of road that we drive is wide open. If the wind is coming from the south then the TT would move the F150 around. Never budged the 2500.
I really think that you're are so close to the physical limits with the F150 that unless you get a Hensley Arrow or Pro Pride you're always gong to be struggling in slightly adverse conditions.