".......rear end seems o.k., "
How did you check it? Easy to do. Don a pair of heavy duty gloves, and with the car on flat ground, grasp each rear wheel in turn and yank in every possible direction. There should be NO freeplay. I think you'll find some, based on your description.
With ours, I assumed handling problem was worn rear shocks and replaced them. Even though the originals had shredded booties and showed signs of leakage, this caused no change in the problem. Did the yank test and immediately found an issue with the right rear. Tightened the loose bolt on the tracking strut, and everything was fine.