RE: the AWD/tire OD discussion, I've heard that putting a significantly mismatching OD on an AWD xDrive Bimmer can cause the car to go into limp mode in order to prevent diff wear.
So it's confirmed the non-M cars do indeed have a mechanical diff? OP, if this is the case and if you only have 25% tire tread left, I would recommend purchasing an additional new rear tire and chalk it up to bad luck - better safe than sorry.
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