OP,
The 250's are notorious for sag under a load, even within spec's. As already stated, you may can adjust some of it out by adjusting the hitch set up. Two things I did that greatly improved mine are.....
1. Bilstein 4600's on all 4 corners.
I know it sucks to replace new OEM equipment, but the shocks that come on these trucks are sub par at best. Even the FX4 package Rancho's are nothing more than Ford shocks painted and stickers that say Rancho. They will work for a while if need be, but many replace them before 500 miles if towing much. Yes, there's that much difference.
2. General Springs (Out of Kansas City Mo.) Custom long add a leaf.
I pull a fiver with mine and even within all specs the truck sagged badly. Like you said, no rake from the factory. This is a long custom made AAL that made a tremendous difference towing! Also, the ride didn't change unloaded much at all. Yes, maybe a touch stiffer, but honestly hardly noticeable. My towing experience improved tremendously with these two upgrades. All of it was done for roughly $500 bucks as I installed it all myself. Now the truck sits basically identical to a 350. And when loaded and hitched up, I sit dead nuts level and dips and overpasses and such are absorbed effortlessly! Otherwise the truck is stock and goes very well. I hope this at least gives you some options if you can't adjust the sag out. It's a shame that mods have to be made to make a 3/4 ton truck handle a 3/4 ton load, but it's a common issue on these trucks in the factory set up.
Good luck and enjoy that beautiful TV!!!