My F250 has a rear GAWR of 6340 lbs and a payload of 3,759 lbs...so we have lots of safety cushion and can carry a generator in the bed of the truck if we want. Another reason to go w/ 2WD if you don't need 4WD to get the extra payload etc. over 4x4.
There is no 250/2500 LDT that can carry 3759 lbs as payload in the bed on the rear axles like a truck camper or GN/5th wheel hitch weight. This is just anothor example of the fallacy of a gvwr based payload for "some" gas powered trucks.
Looking at fleet Ford specs on a 2019 crew cab 176" wb 6.2 gas show around 7 lbs difference in dry rear axle weight in a 2wd vs 4wd.
And around 140 lb difference in dry rear axle weight in a same truck above in 6.2 gas vs 6.7 diesel.
The only way the a 250/2500 truck could carry 3759 lbs is with a bed/front bumper mounted overhead rack like we see on Overhead Door service trucks. The rack allows that 3759 lb payload to be spread over front and rear axles.
Running some number on the OP rear axle shows a 6340 rawr. These trucks rear axle are weighing in the 3000-3200 + lb range leaving around 3200 lb for a max in the bed payload.
