James Pratt added the following comments.
We are using BMW rear gear oil in the differential, I believe it is 70/140 or so. We are using NAPA anti-seize compound on the rear drive splines. Some people say to use moly-based grease in the drive splines, but our very skilled local BMW mechanic recommended this thicker anti-seize compound. He said the moly grease tends to disappear much faster when it gets hot, and the anti-seize is thicker and remains in place longer. The key is just to make sure you lubricate the splines with some type of thick grease in some fashion.
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