I quoted the correct bearing play from the shop manual for a W126. I apologize for not being specific in citing the reference, but as I had researched this on the forum, many others were offering similar advice on setting bearings for many models/years. If this is not the right value for your car, someone else will have to provide it. But .001" is a LOT of play, unless Mercedes has radically redesigned the front axle/bearing assembly.
Did you try Stevebfl's suggestion, which should tell you whether the problem is axle/hub/bearing or wheel/tire?

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1986 560SL
2002 Toyota Camry
1993 Lexus