Wet weights are for units without options so they will probably be heavier than those numbers. Then figure you will be adding a minimum of 500# of stuff in the camper. And finally, you have the weight of people and stuff you put in the truck. So you are looking more in the 5,368 and 5,774 pounds you need to be able to carry.
Even if I go to axle and tire limits with my gasser, the lighter of the two options would overload my rear tires. (My empty rear is 3,020#). So the first thing you would need to do is upgrade to 19.5" tires.
My father has a 4,500# camper he carried for a while on a SRW with upgraded tires. It worked and he never had a problem. But when he bought a new truck this year, with a lot of prodding from his children and others, we convinced him to upgrade to a dually for the camper. First drive with the camper on board and he was convinced the dually was the worth the inconvenience of the dual wheels.
I carry a 2,400# camper with my SRW Ram and don't really know it's there. We are also trying to upgrade a camper but keep passing on even those weighing 3,500# wet as we know they would make the truck a nightmare to drive on back roads.
Don't forget, driving a dually with the camper isn't a problem because the camper is wider than the truck.