If you look at the tire loading sticker on the driver door panel, it will tell you the payload for everything in the truck, passengers, gear, hitch, and pin weight. I'm guessing 2500-3000 lbs. This is more the # you need, rather than how much it will pull.
I think GM under rated the newer 6.0 trucks, with the 3.73 gears. The same truck, with 4.10 gearing may be rated to 13,000#s pulling cap.
I think you should look at a FW with an unloaded wt about 8,000#s, and loaded wt of not more than 10,000.
You can lock out 6th gear for pulling, even 5th if needed, and tow in 4th.
Good luck with your search,
Jerry