First your empty curb weight is more like 6844. Ready to tow is will be in the 7500 pound range. Rear axle will be around 3K ready to tow. So if you ignor the GVWR of the truck and go by the RGAWR you might slide in under the radar. What does the placard state for rear GAWR. The 6800 number sounds like someone is accounting for the installation of LT265/75R16E tires, when most came OEM with 245/75R16E tires rated to 3042 giving a 6K GAWR on the rear. I would be very surprised to see a 6800 Rear GAWR on a 2008 250/2500 anything, Ford, GM or RAM.
So with around 4400 on the front axle and 3K of the rear you will weigh 7400 giving 1800 pounds for capacity based on 9200 GVWR with 3K of pin weight you will be a 10,400 or 1,200 pounds over. That bothers many. Note: This will not work at all with the LT245/75R16E tires. So it if has LT265/75R16E tires are they mounted on wheels wider that the OEM 6.5" wide rims?
This is what a 265 looks like on 6.5" wide rim. Sidewall rolls in way to much for the tire to function as designed.

If your wheels look like this, then they are the 1 x 6.5" wide rim GM has used for years.

Moderator edit to re-size pictures to forum recommended limit of 640px maximum width.