It is, as you put it, an outside and underneath job. There are levers coming through the tunnel underneath, these are connected by rods to other levers on the side of the transmission. There are spring clips that you can push off with a screwdriver. You then pull out the rod and push out the bushing.
I would suggest going under and looking at the bushings. Wiggle them around and see if they are loose.
You probably will find no problem underneath the shift boot inside the car.
'84 Euro 240D, 516K miles
'88 300E 5 Speed
'81 300D Daughter's Car
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