I tow roughly the same weight 5er with a 2500 CTD. My CCC is 2176lbs for the truck. RAWR is 6000lbs. My empty pin is 1385lbs. We load the kitchen sink in the front. I use a B&W Patriot. Our 5er is 8800-9000lbs loaded. The loaded pin is apr 17-1800lbs. I'm over the trucks GVW by 200lbs. Big deal. I'm under the RAWR by 1100lbs. Good deal.
20% for pin weight is the norm. If you're around 8200lbs loaded then 1640lbs would be the pin weight. You can get an Andersen Ultimate 5th hitch that only weighs 75lbs. No need to figure 150-200lbs for a 5th hitch.
IMO to the OP load it up and go. You will maybe be over the trucks GVW a little but well under the GCVWR.