Your problem has a lot to do with the frontal area and that will carry over to any truck, though you are working the 2.7 a lot harder than it was meant to do continuously. The main way that the F250 will help you is if you get the 48 gallon fuel tank.
All Ford pickups are rated for 60 square feet frontal area bumper pull, 75 square feet with a gooseneck. The reason for the higher rating on the gooseneck is that it is closer to the cab and gets less direct wind on it. When my daughter switched from a bumper pull horse trailer to a larger and heavier gooseneck her fuel economy went up You would probably do well to get a camper shell that rises up in the back to maximize air deflection around the trailer. Or a gooseneck trailer with some aerodynamics up front.
See page 16 of the towing guide:
2021 Ford towing guide.Are boats are probably at the 60 square foot frontal area but the pointed bow and raked windshield help reduce drag.