New truck, New trailer, TONS of sway!

I have a LaCrosse 329 that weighs over 10K pounds when loaded with all of our junk, propane, batteries, etc... I started off with a 2014 GMC 1500 CC with LT E rated tires, and heavy shocks with a Curt Pro Series hitch and dual friction bars and it was not pleasant. The truck had enough power and brakes, but it was a case of the tail wagging the dog. Ended up moving up to a Cummins Ram 2500 CC 4x4, and while it was a LOT better, it still got pushed around on very windy days. I recently got a Hensley and the difference is amazing. When coming back from our last trip we had heavy interstate traffic and 35MPH side winds and everything felt rock solid. It was actually relaxing at 70 with the cruise on.

Before spending the money on a new truck I would look at getting a Hensley or ProPride hitch. If it makes the F150 work with the trailer you will be ahead, and if you do end up moving to a bigger truck you will have the ultimate setup.