Well, no idea on what's happening to my Runner. Chassis to body bushings? Rear suspension specs too close to limits? Shocks are not the case, not even wheels nor tires cause the problem was still there after replacing those.
Do a test, go over a speed bump at the normal speed you usually pass over them and check for side to side movement once the rear tires pass the bump. That's something I noticed just after replacing the coils. And yes, it moves much better in general, just be careful when traveling at high speed, they get unstable once you lift em'.