Great Question and has been a problem with the 4th Generation Rams from inception due to the OEM 4-link attempting to give the plush ride unloaded of a cadillac yet still do minor hauling duties.
The best remedy will be stiffening the designed flexible joints which when torque transfers clockwise from the tires, the reactive force is on the lower rear control arms as the axle tries to twist and compress them through the frame mounts. However, if you have an open rear end and one tire loses traction around the corner the sway and track(panhard) links become the weak points. Lowering helps keep the center of gravity down as well to minimize this effect. Running a better dampening shock like the 4600s will certainly be a noticeable improvement as well.
My tires stayed on the ground the entire time upgrading uppers and lowers, but swapped one at a time and needed a jack on the pumpkin(only the lowers) to center the holes as the OEM arms were stretched slightly from center to center. You'll want a breaker bar for the lowers, the 200 ft-lb torque spec is accurate and should be tightened as mentioned with the full weight of the vehicle on the hardware.