I would check transmission mount first. The slight rocking of the transaxle as the car shifts from power on to power off could be responsible for the noise. The engine also torques from left to right as power goes on and off, so engine mounts (a known problem on these cars) could be shot and allowing something to contact the torque tube tunnel or even the exhaust system. Have someone watch the movement of the motor as you go try to go forward and reverse while holding the brake.
Pro tip: Have then stand off to the side to minimize the chances of getting run over.