"BAD TRACK ROD MOUNT(S) AND BUSHINGS!
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That's interesting as a W124 doesn't have track rod bushings...!

I'd pull a bolt and check the dampener for resistance. Any front suspension play can do... with the wheel brgs properly adjusted, new bushings and ball joints? Strange you listed those seperately as they are as the ball joints are welded on the lower control arms(which come with new bushings). What brand of control arms did you buy? Febi or MB or china made? Pulling on the wheel with the car on stands.. there should be no play.
With the car running and in park. If you take the wheel and move it 3-4 inches back and forth quickly- kinda violently. Does it make any noise? Clicking or abnormal sounds.. My car has a vibration at 80-85 mph and I think it might be the box.
The earlier cars have a TSB about possible steering box bolts becoming loose. They are stretch bolts(don't loosen them), but make sure they are tight by applying the FSM torque.
used low mileage steering boxes are cheap- $100-125, plus you can re-seal them first for $20 in parts. V8 boxes seem to be more prone to leakage than L6's.
Michael