I wouldn't at all be concerned about the ability of a Ford F250, or any full size pickup's ability to accommodate the load. I've hauled every size bike in the back of a pickup from old Triumph twins to a Harley Electra Glide.
I just tried without success to find the pic of one of our members, Elcanaco, off loading his Ultra from his Chevy half ton in my driveway. Gord probable stands 5ft 6 inches and weighs in at about 160 pounds.
The ramp is the key and if you don't have access to a good set of motorcycle ramps, I wouldn't even try it. I have three part, 10 ft arched, folding MC ramps that I put in the back of the pickup with the bike to use at my destination. I ride the bike up the ramps into a Condor, or other suitable chock such as a Pingle, and then back the bike down with my hand on the front brake. A spotter at the bottom is important to helping keep the bike centered on the ramp. It also helps if you can find a high spot of ground on which to set the foot of the ramps.
With the above said, I don't do it anymore. At my age everything seems riskier.
On the trailer, U Haul has two suitable trailers. One is actually designated a bike trailer while the larger one an open cargo trailer. The latter has a cutout in the front for a motorcycle wheel. It has many tie down points an an excellent ramp. It was actually cheaper to rent than the MC trailer. Had pic of it with my Rocket in the trailer and my VStrom DL1000 in the back of my Titan pickup, taken when I hauled both down to Monterey, CA to give to my son.