I know a guy who bought a 1984 F-150 with a slim cargo rating, and 351" engine. He was looking at travel trailers with a 750 pound hitch weight, but ended up with a 24' Wilderness fifth wheel, I would guess it might have had a 1,500 pound pin weight, it was tiny compartment for sleeping up in the front (think camper cabover, not really the walk in style of today).
Anyway it is possible to tow way more trailer than the truck is 'rated' for. Yes you could tow fine with a 2,000 pound hitch weight, and still not go anywhere close to the tire weight rating on your rear tires.
What is your front and rear axle weight? My guess is with a 6,900 pound overall weight, that about 4,000 is on the front and 2,900 on the rear axle as it sits. That leaves around 2,500 more that you can safely add to the rear axle, however it will put you over the GVWR. Are you worried about warranty problems with a 7 year old truck? I would not be either. Basically it is similar to the 3500 truck that you should have bought. . .
Anyway you will know better with the next pickup. . .
Fred.