I used to tow a 34' trailer with dry weight around 6800 lbs. Tow capacity of my 2003 3/4 ton was 8800 lbs. I definitely knew it was back there, although the 5.7 worked just fine. We used a WDH with a built in anti sway, but honestly we rarely encountered wind or semi's passing. When I did, it was a little bit more white knuckle although not too bad as I towed @ 55 mph. You may have a lot less fun, considering the lighter tow vehicle.
Also I'm curious what F150 has a CCC of 2461 pounds, even the 4x2 supercrew shows around 2000 lbs. May want to double check that spec.
2016 F150 towing