I'm totally unqualified to say, but my best guesses, in order, are:

1-belt tensioner and damper
2-water pump
3-transmission (not really but see below)

All of these are 100% covered under your Starmark. Take it to the best dealership facility around, forget about cost, tell your service adviser "it's shaking", be cool about it, and ask when you can pick it up.

BTW, if I were you, with the goal of MBUSA installing a new, updated transmission, I'd try to have the transmission declared problimatic. If you search under 722.6 I think you'll see.

Good luck and best regards,

__________________
Michael

1988 300 SL (5 Speed)
1994 E320 Wagon
1997 C230