Well, if anyone is interested, here is what was finally discovered to be making this really annoying noise:

Both rear differential to subframe mounts were apparently completely shot. So how about that? This car has 110K on the clock.

Took it to a reputable independent after exhausting all possibilities (that I could reasonably DIY in the dead of winter)

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1995 MB E320 Wagon
2001 BMW 530i
2007 MINI Cooper S (!)