I still believe that your "shaking" is tire related. If you want to check your steering components, raise the car in a safe manner. If you have nothing to work with except the MB jack that came with your car, it won't be safe enough. If you do have the equipment to do so, you should be able to raise both wheels off the ground. You then should be able to shake and pry on your steering components to check for any play.
I'm a bit skeptical about these all being worn. My 240D still has the original idler arm and centerlink. I've replaced the tie rod links only a few weeks ago. If these components are loose, fine, they need replacing, but I wouldn't expect them to cause the shake.
'84 Euro 240D, 523K miles
'88 300E 5 Speed
'81 300D Daughter's Car
Over 800,000 miles in