Alright, so the upper control arm itself was good, but the bolts were trash. Got these replaced. Had the car re-aligned, and it looks like the previous alignment job was pretty shoddy; there is no pull upon hitting bumps with rear wheels anymore.
It looks like the original problem is back, at least in some capacity. The car still feels oddly loose when swerving, especially to the right. It almost feels like the car's "pivot point" (not sure if that's even remotely close to the proper term) when turning is shifted from the front more towards the center of the car.
The rear lateral links (along with the stab links that I have replaced) were a very good guess, and that itself has contributed to ride quality improvement. Any other guesses, suggestions?