UPDATE:

The source of the vibration was not the engine; not the engine mounts; not the transmission mount; and not even to a great extent -- although some -- due to the broken exhaust hangars.

It was the crap axles, i.e., GKN Loebro, that were installed.

Hearing GKN called "crap" may surprise people but, in my experience, they are, with *three* failures in 2 years! (Inner boots torn off.)They were problematic from the start, vibrating strongly when the car was in gear.

The worst was the left side and I decided to replace it myself this past weekend after the inner joint separated, with no effort, when I was replacing the wheel hub and bearing the prior week.

I bought a Cardone remanufactured axle for one reason: It was about 20.5" long, which I believe is the correct OEM length; vs the GKN and other aftermarket brands, which are about 19.5" long. I am convinced that is the reason for the inner boots tearing (all three times) and the vibration. The axles were too short. New, 20.5" reman axle is quiet and vibration-free.

I still have the other GKN on the passenger side, it is still vibrating but I don't feel it as much, and will replace that with genuine Mercedes since their passenger-side axles are oddly affordable (~$275 to $300) at the dealerships, after core.

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2008 E350 4matic / Black/Anthracite

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Gone but not Forgotten:
2001 E430 4matic, 206,xxx miles, Black/Charcoal
1995 E320, 252,xxx miles, Black/Grey
1989 260E, 223,00 miles, Black/Black