The steering shock can certainly be the culprit, but, you mentioned that you believe that it's OK? Is it still original.........how did you confirm that it's OK?

Unbalance in the tires and any out of round condition in the tires will definitely cause vibration on a W126. In fact, a perfectly balanced tire and wheel combo can cause some definite vibrations at discrete speeds if the tires are not round. In this day and age, where tires cost less than they did 20 years ago, the roundness of a particular tire is certainly a concern. This roundness is never mentioned by the manufacturers or the dealers, yet it can be a significant issue.

See if you can mount a piece of chalk or a pencil point on the floor so that it contacts the tread. Rotate the wheel so that the point just contacts the tread at the highest point of the tread. Now rotate the wheel 180 degrees and look at the gap. A very good tire will be 1/16" or less. A poor tire will be 1/8" or more. You'll feel 1/8" on a W126.