The rear mount as you suspected is usually the problem here- yours may move a lot more than that under load. They're cheap, I'd replace that. If the front mounts are also worn, your engine may move a lot more than it should- the way to tell is if the oil filter is very close to the frame, or if you can see that the mount by the oil filter is sagging & distorted. When you get new ones you can get German or Swedish- the German ones are much firmer but transmit more noise to the body.
The exhaust may well have a broken hanger as well. Look to see that both ends of the rear muffler are secured, and the pipes aren't broken anywhere. They typically fail right behind the right rear wheel. There are also rubber mounts just in front of the axle, on the front muffler- check that these are all attached as well. A loose exhaust system makes all kinds of racket under the car.
Good luck!
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Rob Bareiss, New London CT ::: 86 244DL, 87 244DL, 88 744GLE, 91 244: 808K total