F250 gas trans is different.
I'd suggest not considering the 250 for that weight. Got for the 350 and get the 4.30 gearing. But do some homework on the tongue weights of that trailer. Given the GVWR of the trailer I'm guessing its a gooseneck. Even 20% of the GVWR is 3200#. Add a couple humans in the truck, some gear and some stuff in the bed and your going to be up against or over the GVWR of a SRW 350. If you go over to ford-trucks_com there is a guy with a 6.2 dually driving as a hot shot. Might be something to consider. Sure, a diesel dually is ideal but how much will be be towing and is the premium price for the diesel engine feasible.
Happy Trails