Ummmm..... River&Sand, respectfully, you negelcted to include the weight of the truck itself in your example.
This TC will exceed GAWR rear and GVWR before adding any owner stuff.
Curb weight of a 2002 1500 reg cab long bed is around 4200lbs,
So if you say the weight distribution is 65/35 front/rear, that means 2730 is on the front and 1470is on the rear.
So GAWR Rear = 3686-1470 = 2216 before maxing out. Since the OP states the CG of the camper would be directly over the rear, that means all 2400lbs sits over the axle exceeding it by almost 200lbs BEFORE adding any passengers, food, stuff.
GVWR = 6400 - 4200 = 2200lbs max payload. The camper is already 200lbs over this.
The GVWR of theis older non HD 1/2 is just to light for a hard side TC. And by the time you take a passenger and add all your stuff you will not be exceeding the GAWR and GVWR numbers by a little, it will be by A LOT. MAYBE a very light pop-up TC would work if you can find one that weighs about 1000lbs less, around 1500lbs. That way when you add your stuff and yourself you will only be exceeding these numbers by a little
Can you do stuff to the truck to make it work? Maybe. Airbags, overloads, sway bar, D rated tires, etc, but you still have the semi floating axle and brakes of a 1/2 T. All those mods will also begin to get almost if not more expensive than selling the truck, adding the money that you would have spent in upgrades, and get a good older 3/4 T.
