Your alignment is fine, might be a little taily on the track but that can be fun (personal preference). Plus, alignment would only create instability at the rear if there was a lot of toe out.
So, I reckon there is a problem in the toe control. Start at the centre and make sure the lock bar is bolted down securely, then check the inner tie rod ends are tight. But I reckon it's almost certainly stuffed ball joints at the outer/hub end of the tie rods. That was the issue I had, and I had exactly the same "tail wagging" feeling. Unfortunately they are both painful and expensive to replace, I could not find an aftermarket option