A GAWR of 3900 lbs is a meaningless number unless you weigh the truck itself. If the truck with the best empty weighs in at 2,000 lbs. then the load capacity is 1900 lbs. minus the 250 lb. weight of the receiver or about 1600 lbs. at best.
There is also the load capacity of the tires on the 1500 class trucks. With my 2500 truck the factory tires were rated at 3195@80 PSI or 7190 in total. I replaced them with tires rated at 3750@80P PSI to gain an additional 1100 lbs. of payload capacity.
Taking 1600 lbs. for the bed load capacity, and assuming the tires can each support 2000 lbs., then the loading 5th wheel would need to have an empty weight of 6000 lbs. or less. Go to any place selling 5th wheel trailers and see if you can find one that is less than 6,000 lbs. dry weight. They do not exist and for good reason as it would take a very dumb person to buy one.
It is far more sensible with a 1500 truck to go with a travel trailer where less load is placed on the truck's rear axle and wheels. If you want to tow a 5th wheel trailer then the smart thing to do is buy a 2500 class truck (excepting the Power Wagon) that has the stronger frame that is made for adding a 5th wheel receiver and has better brakes and great payload capacity right from the factory.
With a 1500 pickup the smart thing to do is either buy a travel trailer or a light pop-up slide in camper. With either choice the OP will be able to find a buyer when it comes time to sell it and move on to another RV.