[1955Joe]

My son described his 97 LeSabre, 130,000 miles, symptoms to me similar to yours. He had a slight thud after the initial acceleration and a slight thud when he let up off the gas. He did not tell me until after it was fixed the whole car would vibrate and that it scared him.

So we took the car in to have the transmission mount and 2 engine mounts replaced. The real problem was a front subframe bolt was no good and the vibration was that the body was coming off the frame.