My 92 500 SEL started to vibrate at 40/45 after three years, it got better as it warmed up. Mb replaced control arms, drive shaft etc, and balanced the wheels on the car. I came back after rotating tires.
The dealer suggested motor mounts (one was collapsed) did that, no big change. They next suspected the lower control arms (hydraulic mounts) slight change. I got rid of the Michelins and got Firestone Turansa LS, (roadforce balance) and had the sway bar bushings replaced along with the steering shock. The side to side wabble seems to be gone.
I would probably start with the bushings first, since the steering daper had been replaced previously.
That was my experience I hope yours is not as expensive, I wanted to dump the car but my wife loves it