U Need to Re-Check
Don't want to get in any contests here but I thought the same thing until I got on Fords Build & Price site. As you build your car they state & change the Tow capacity and Payload as you add and delete options. I agree about the weight you posted but I think that is for the gas engine. You loose upwards of 500 lbs of payload (I don't remember if tow weight changes) when you add the diesel.
I just did a build and price on a 2014 SD, crew cab, 4X4 with the diesel and the payload is 2620 lbs and tow is 15,900 lbs. Try it. The payload numbers and tow capacity are just to the right of the changing price as you add and delete options. I found this out at the last minute and got a F-350 with an 11,500 GVWR. Not saying your rig wont do the job, just trying to make you aware of the specs.
2013 Ford F-350 SD Diesel, 4X4, Crew Cab, Lariat
Sabre 2014 32RCTS, Pullrite Superglide 2900 18K