I would disagree with not enough truck. Sounds to me like the hitch is not set up correctly. While the 3.31 gearing is not ideal it should work.
Here is my recent experience with my 2 month old 2014 F-150 Supercrew 4x4 Ecoboost with the 3.55 gearing and tow package. Last weekend I towed my 2006 Rage'n FS-2500 toyhauler with a 2006 Arctic Cat Prowler side x side with a full cage w/ metal top, 4 seats,over size DOT Super Swamper tires and wheels, full gas tank and more. The trailers 80 gallon water tank was full as was the propane and it contained food and supplies for 16 people for 4 days camping. We towed from Phoenix to an altitude of 7700+ feet in windy and rainy conditions. The truck bed was also loaded with extra propane cylinders, a 3 burner Camp Chef stove, 4 cast iron dutch ovens, cast iron griddles and frying pans, steel dutch oven tables, charcoal, fire wood, tents, coolers with 80 lbs of ice and more.
I have the Equalizer square bar WD hitch with 10k bars which is very similar to your hitch and spent a full day the week before setting it up properly. I was amazed at the factory sway control, I could actually feel it correcting the truck when passing through windy canyon passes with strong crosswinds. I was never white knuckled once compared to my 2006 F-150 with every tow option at the time and a Prodigy controller on the same trailer which was a handfull.
The Ecoboost was only turning 1600 RPM at 60 MPH on level ground in 6th gear and never dropped below 4th gear in the mountains at 3500 RPM at 50 MPH. Between the Ecoboost (which you don't have), the 6 speed transmission with Tow Haul mode and the built in sway control, both of which you do have, I am 100% sold on my purchase. Again your 3.31 is not ideal for towing but with your trailer weight it shouldn't be a problem except in hilly terrain. I had people tll me my 3.55 gearing wouldn't work either but my Nephew has been towing a Jayco 26' toyhauler with a Polaris Ranger in it all over Arizona and Utah for two years with a F-150 Ecoboost with 3.55s and has been thrilled with it. He sold a Duramax diesel for the Ecoboost and said it was worth it.
Have someone double check your WD hitch set up. I talked to a guy yesterday who added an additional friction type sway bar to his hitch but I can't imagine needing it the way my trip was last weekend.