The synthetic gear oil will clean much better than regular dino gear oil.

My suggestion is to fill up with the Mobile One gear oil and continue to observe the recommended 30,000 mile change interval. You could cut that short for the first change if you wanted, perhaps after a year of use if you don't put 30,000 miles a year on the car.

If you clean the gunk from the bottom area of the differential that you can reach, that's plenty clean.

Ken300D

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1982 300D at 351K miles
1984 300SD at 217K miles
1987 300D at 370K miles