Right, NOT worn out.
These old engines complain a lot before giving up the ghost. Hard
starting, low power, oil consumption are the signs of the end. Your
engine, despite its 300K miles sounds like it's in good shape - no doubt
due to good prior maintenance.
I'd suggest you dump the mechanic who claims the engine is tired. He is
looking at its mileage rather than at its condition. In his favor is
that most engines of this mileage would need an overhaul by now. Yours
is the exception that may go to 400K if you take good care of it.
By the way, with a 10 mm and either 12 mm or 14 mm wrench you can adjust
the rack damper pin. It looks like a small bolt screwed into a nut (lock
nut) on the aft end of the engine's injection pump. Look between the oil
cooler lines at the back end of the injection pump.
The larger nut is a lock nut, the smaller bolt is the adjustment. Loosen
the lock nut one half turn. Then screw in the bolt on half turn, hold
that position with the wrench while you snug the lock nut tight. By
tight I mean firmly snug, not tight as in all your might tight. This is
an incremental adjustment, more may be needed but first drive the car
for a while. Too much tightening will stall the engine, if so, back it
off. If the bolt is screwed all the way in and no further adjustment is
possible the pin ought to be replaced, the newer version has a stiffer
spring and is more sensitive to adjustment.
My 300SD used to shake - a lot, particularly at a stop light after
exiting the freeway. This adjustment and a new pin completely cured
Finally, the engine's shaking won't harm the transmission or its mount.