That misconception was discussed on forum about milion times and still comes back.
Sticker payloads are taxable numbers and have no practical use for TC and towing.
250 tongue weight will add about 350 lb to your rear axle and rear axle is the only worry with such combo as trailer actually takes weigh off from front axle.
So proper procedure is
-check rear axle rating
-weight what empty truck puts on the rear
-calculate how many lb TC will put on the rear. With short camper you can estimate about 90% going on the rear
- having above calculations you can figure out if you have any capacity for tongue weight left.
Here is online calculator that can help you. Why you don't see many towables behind TC ? Might be several reasons, but fact is that most of TC buyers are looking for luxury, so they always buy the biggest campers they can fit on the truck, often even exceeding truck capacities.
Few members here who have big camper and still tow, bought F450 or F550 for the job.
