My 4.4 is having the same noise but relatively much diminished. I have to turn off audio, a/c and close all windows to hear it. Does yours make the noise when it's stationary or only when it's on the move?

From your investigations, the noise could also be coming from the pulleys or the belt, not necessarily the alternator itself. I would spray mist of water on the pulleys and belt to see if the noise goes away, in which case the pulleys/belt are the culprit and would need replacement.

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'05 E53 X5 4.4i, '97 E39 528, '07 E92 335i, '16 F86 X6M.