The payload is determined by the tires. Put two Nitto or Toyo tires rated at 3750@80 PSI and you have 7500 - 3000 (weight of your truck on the rear tires) or 4500 lbs. of load capacity in terms of the axle, wheel bearings, and tires.
If the camper weigh causes the truck to sag in the rear then for $500 you can add a set of SuperSprings that will take an hour to bolt in place. No different than the 3500 that has a second leaf pack on each side.
With a 4500 lb. maximum payload you can stay at 4,000 lbs. maximum with gear, food, water, etc. and go with a camper that has a true dry weight of 3,000 lbs. and there are many to choose from.
1000 lbs. may seem like a lot to allow for "extras" but the Lance weight does not include an AC, a second battery, a roof rack, generator, solar panels, or the weight of the fresh, gray, and black water tank fluids at about 8 lbs. per gallon. Add a generator and fuel or tow a trailer and add a heavier duty hitch and a stinger and it is easy to push the boundaries.
The other $3500 option is to get Rickman 19.5 rims and 19.5 tires at which point you have a rear load capacity of 8800 lbs. minus the weight of the truck. Not cheap but a better option in many ways than DRW.