The front/rear diffs would only be effected if different diameter tires were place on the SAME axle, not front/rear stagger.

Front/rear stagger effects the transfer case, you have an open transfer case and you have ZERO front/rear stagger with the same size tires all around.

Tires had no cause connection to trans failure.

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'03 X5 4.4 Sport, last of the M62s (8-03 build date)
I believe in deadication to craftmanship in a world of mediocrity!