I just bought the same thing you did, F250 with the 6.2 and a 3.73 rear end.
I would not hesitate to get a ~9500-10k lbs 5th wheel. Truck is rated to pull 12,100 with the 3.73 rear end. So at 10k, you have a 20% margin, which would make me feel very comfortable.
GCWR is 19000ish. Tranny is pretty heavy duty. Next year, the gas F250 is supposed to get some tranny that was left over from when the F150 offered the 6.2 L motor a couple of years ago. This is the reason I bought a 2016. Still had the Torqshift in the 6.2 L gas.