The 7280 load rating for the two rear tires is your real limitation. Minus the 2730 that leaves a wet camper (with fresh water in the tank and all your gear) of 4550. I would be looking for a camper with a "dry" weight of 3,000 lbs. or less which may be the case with the one you found. For a ballpark weight look at the Lance sticker on the back of the camper for the weight and add 500 lbs. for a probable dry weight - you can verify later at the scales.
Allow for the cost of tie-downs and turnbuckles, 7-pin connector and battery isolator, extra springs, heavy duty shocks, and probably a rear anti-sway bar, in totaling up the cost to get this camper on your truck and heading down the highway. Suggest doing the suspension mods one by one and then evaluating handling before making additional ones.
Home Depot sells 4x8 foot pink insulation panels in thicknesses of 1" and 2" and they do not compress under a camper load and do not absorb moisture. They are the easiest way to raise the height of the camper. I put one sheet on my bed liner and then a rubber mat on top of the foam and then my 4,000 lb camper which does not slides at all.