I had something similar happen to my 86 300E after being rear-ended. I went to pull it off the road and suddenly heard this clanking, banging sound that I, too, could feel through the shift knob, even though it's an automatic. Similarly, after backing up and pulling into a parking lot it went away, for a short while.

Turned out that the impact tore loose the front flex disk and it was spinning out of round and out of balance whenever the car was in motion. Backing it up apparently realigned it temporarily, but as soon as a little bit of torque was applied the banging was back.

Perhaps you let the clutch back out a little too rapidly and in trying to spin up the engine the force was too great and the flex disk let go. How many miles are on it? Have the shop get it onto a lift and check the condition of the flex disk(s) and see whether or not the driveshaft spins true.

The front disk is a bit of a pain to replace and from what I understand is the one most likely to wear out first. Mine let go at a little over 112k mi. Don't know if it was the original but I suspect it was. On a manual trans car I would expect it would have a shorter lifespan than on an auto.

Hope this helps,

Gary