2008 F250 6.4L TD, 3.73 ratio, crew cab, 4WD

My Truck: 2008 F250 Crew Cab, 4WD, 6.4L TD, 3.73 Gear Ratio

I'm told by the dealer that the max towing is 15,200#.

Am considering the purchase of a 5th Wheel Travel Trailer that will push (ok, exceed) those limits and am wondering what to expect, if anything. I've never towed this heavy.

Dry weight on the unit is 14,315.
Hitch weight is 2,797
GVWR is 19,000

Full water and waste tanks alone will put me at 15,500, although it would be unusual to tow with all 3 tanks full.

5.5kW genset is going to add 279#

Unsure how much fuel it holds at present.

In only the rarest circumstances (hurricane evac) would I ever foresee myself needing to load it to 19000 and even in that occasion it would likely be closer to 17000-17500.

Typical usage would be weekend camping trips with the family. No ATVs or motorcycles in the cargo area.

Terrain is rather flat with some large bridges to cross. Average tow 3-4 hours drive time. Longest anticipated tow would be 12 hours.

In YOUR EXPERIENCE would I be making a mistake and why? Or, can the truck handle it without a significant problem.

Buying a dually is not in consideration.

Thanks in advance for your help!!