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