I don't have a similar trailer. Well I do, a 28' enclosed v nose running around 6klbs.
But I did have a 2011 F150, light duty, XL 5.0 as a company truck and I can say I towed a whole lot heavier than that with it and the 5.0/6 speed combo has enough power to keep you running with traffic, even up most grades. 10 years ago, I'm pretty sure that was the best towing combo in a half ton, save for maybe the Vortec Max GMs.
For long distance and high profile like a TT, I would still feel comfortable with that truck.