My thought is vibration due to tranny mount. If it is spongy and soft feeling, replace it. That's where your wiggle is coming from.

The Benz drive shafts seem to be sprung to self-centering. My mechanic notice this "weirdness" when changing out the center support bearing. The shaft doesn't hold a kink, it'll straighten itself out on the bench.

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Cheers!
Scott McPhee

1987 300D