^^^Yeah, it's safe to say with diff and lock in it, it's related to the e-diff which you're certainly running.
If I had an ice-skating rink handy, I'd run out, shut it off and test it right now.
But I have been drinking...
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'02 S54 M3 (500/500 GC/Koni)
'08 N54 135 (JB4, DCI, BMW PS/Bilstein B6s, H&R M3 FSB, Strongflex FCABs)
'14 N55 X1 (JB4, BMS DP, BMS Intake, Alpina TCU reflash, H&R Sports, Bilstein B6s, E93 M3 RSB, Strongflex FCABs, baby seat)
'08 N54 535xi touring (Bilstein B6s, Downpipes, MHD tune, baby seat)