With an F-350, single rear wheel, 172" wheel base truck with 6.7L (4x2 or 4x4) you are over weight and do not have a properly configured truck, for the pin and loaded weight of your fifth wheel, in order to safely tow your 5ver you need a DRW truck, and you may need to step up to an F-450 (if you stick with Ford). The maximum fifth wheel trailer weight that Ford lists includes the weight of the trailer loaded with cargo (water, holding tank levels, camping gear, food, etc...) passengers, and anything else that's loaded in the truck reduces the maximum trailer weight that you can tow. Maximum weights listed take into consideration the weight of the loaded trailer, the truck and any passengers and cargo loaded in the truck.
The following is taken from the 2017 RV & TRAILER TRAILER TOWING SELECTOR Towing Guide | pages 23 & 24, page 25 lists the same information for DRW trucks and the maximum weights are significantly higher than what a SRW truck can safely tow and is rated for.
Your best bet is to sit down with someone at your local Ford dealer and have them break out the books for every standard and optional item for everything that will be in the truck you need to have, to safely tow the fifth wheel you have.
Automatic Transmission, CREW CAB, 176" wheel base, 8' bed, SRW Maximum Loaded Trailer Weight (lbs.)
Axle GCWR WB 4x2 176" WB 4x4 176"
Engine Ratio (lbs.) 8' Box
4x2-Axle Ratio: 3.31 GCWR 28,700 lbs, maximum loaded trailer weight: 20,800 lbs (4)(5)
4x4-Axle Ratio: 3.31 GCWR 28,700 lbs, maximum loaded trailer weight: 20,400 lbs (1)(2)(4)
4x2-Axle Ratio: 3.55 GCWR 28,700 lbs, maximum loaded trailer weight: 20,800 lbs (4)(5)
4x4-Axle Ratio: 3.55 GCWR 28,700 lbs. maximum loaded trailer weight: 20,400 lbs (1)(2)(4)
(1) 18" Tires. (2) 20" Tires. (3) Optional 10,000-lb. GVWR Package (68D). (4) Gooseneck tow rating shown. 5th-wheel tow rating limited to 5th-wheel hitch rating of 18,000 lbs. (5) 17" Tires.
Note: Trailer tongue (trailer king pin for 5th-wheel towing) load weight should be 10% (15% for 5th-wheel towing) of total loaded trailer weight. Make sure vehicle payload (reduce by option weight) will
accommodate trailer tongue (trailer king pin for 5th-wheel towing) load weight and weight of passengers and cargo added to towing vehicle. Addition of trailer tongue (trailer king pin for 5th-wheel
towing) load weight and weight of passengers and cargo must not cause vehicle weights to exceed rear GAWR or GVWR. These ratings can be found on the vehicle Safety Compliance Certification Label.
F-350 SRW SUPER DUTYģ PICKUPS 5th-WHEEL/GOOSENECK TOWING
The URL for the pdf file is: (www) fleet.ford.com/towing-guides