Sounds very unpleasant SPW and I note your expert eye ... In the early days of the A340-600 they had that problem as the tail was moving in a Dutch roll (if I recall correctly) and Airbus had to tweak the programming of the control surfaces to stop it. I have been in the back of a 346 twice (LHR~JFK~LHR) three years ago and felt no such problem. But it might be a similar problem.