Just an idea, but have you checked the motor mounts? Depending on their condition, they would cause the engine and transaxle to rock during moderate engine load, imperfections in the driving surface and sudden changes in speed. Take your car to a Midas or a similar shop. Many times, they can tell you what is wrong and not charge you for an estimate. Just go to a place that you trust, think about getting multiple estimates from different places and insist they show you what is wrong while it is up on the lift.