Depending on the year & model, the F series Superduty trucks have an optional integrated trailer brake controller. This controller is the best brake controller that we've used in over 30 years on any vehicle.
As well, what is the rear end ratio & type of transmission? If you google Trailer Life towing guides, you can look up the towing specs for your specific truck.
The F250 with the 5.4 will probably handle your 27' Overlander. We owned a 74 31' Sovereign
, which weighed in at 6900 lbs fully loaded for travel. We towed it for a few years with a 95 Chevy 2500 with a 5.7 liter V8 (pre Vortec) This combination did fine on the flat - greater than 6% grades were a problem, though, as the small block V8 lacked the torque to dig in & climb. This was especially a problem if we had to slow down going up a hill. We travel mostly in the west, so yes, we do climb the Rocky Mountains!