Livin Lite website says the 6.8 model weighs 1780 lb dry. Probably 2500 lbs after loading.
The 7200 GVWR F150 shows to have a small 3850 RAWR with P tires. These trucks can have a rear unladin weight in the 2300-2500 lb range = a 1350-1550 lb payload on the rear axle.
Keep in mind a payload sticker is determened by the 7200 GVWR number so the 1625 lb number on the door jamb is to be placed on the trucks front and rear axles .... not just the rear axles. This is the downside from high GVWR and small RAWRs.
The P tires load capacity on a truck is required by fed regs to be derated by dividing its capacity by 1.1 percent.
(example) A 2500 lb rated P tire will now be 2273 lbs capacity. LT C or a D tire on higher rated wheels is a better choice.
I'm not sure what the Fords rear axle is rated at but most semi floating axles don't like to be ran in a overloaded condition.
I would look at a lighter weight camper to fit your trucks small 3850 RAWR ratings. I sure wouldn't carry weight above the axle makers max weights.