Cool. What I found jives with that for crew cab, long box, 4x4, srw, Cummins: 7k rear GAWR, 2970 base weight so about 4k to play with for the camper. Crazy that your truck weighs nearly 8000 lbs!Camper dry weight is 2,400 lbs, I have a payload capacity of 4,480 lbs total with 4,100 lbs of that of that being the max rear axle load. Should be well within the rating once gear/water is added.
http://www.rambodybuilder.com/2017/docs/ram/rammlup3500.pdf