You should be just fine with any 3/4 ton (2500 type) towing only 7250 lbs max travel trailer with 3.73 gears.
My wife has a 09 Chevy 2500 CC 4x4 3.73 with a primary use of towing a horse trailer about your weight or sometimes more. We bought the truck new & never have thought we could have used a lower gear.
I was not aware any Ford F250 trucks had engine/cylinder deactivation technology.
We are about to start full timing & just purchased a 42 ft pusher & looking at a Ford 150 to flat tow. We will have a Remco lube pump installed. Please share your thoughts and experiences pulling this size vehicle. I would appreciate any advice you can share. Thank you for your comments??.
The F150 needs to be 4WD to be towable with the above posted directions