Bud, do you know what BMW's service interval is for the differential lube.
As for tips, the classic is to remove the fill plug before removing the drain plug. If the fill plug is stuck then you can retreat and fight another day as long a there is fluid in the differential.
You can get the 14mm (I think) hex socket that you need at Autozone in a set of three for about $10.
You'll need a short piece of tubing to stick in the fill hole and on the bottle of lube.
Be sure to use jack stands when under the vehicle. You may have to lean on the wrench pretty hard. Make sure the wheels are chocked.
1984 300D Euro