2hybrids

My 2008 400H has 158,000 km and started to run very rough during acceleration. A little vibration up to 60 kph and almost unbearable when accelerating from 60 to kph. When you let off the accelerator it stops vibrating.

I bought the car used from a Toyota dealer and have always had them service it (my wife drives a 2011 Prius). The technicians had some issue diagnosing but finally said it might be the transmission and it is $6,000 to $7,000 (Canadian) to replace it. Another tech thought it could be the rear differential. After 4 hours at the dealership no one felt confident in what was wrong. The good thing is that they did not charge me anything!

To me if feels like it is vibrating in the back not the front.

I have had no luck finding anything similar on any forums and even the dealer seemed perplexed.

Any suggestions?