Do not calculate off of dry weight, calculate off of fully loaded, food, clothing, essentials, dishes, tools, chairs, water etc. This all quickly adds up and can push you close to the 16000 lbs which will between 3400 to 4000 lb pin, too much for the 2500.
I pull a 16400 lb fiver with my '08 Duramax DRW and added StableLoads to smooth out the ride and steady the truck going over road undulations. My 3500 only squats 3" with the load, now 1" with StableLoads, and pulls the trailer effortlessly.
I would look at a lighter fifth wheel if it were me.
Good luck and happy camping.