Never updated this thread so just to update it - in the beginning of winter I disassembled the LSD once again and rechecked backlash and tension etc, have flipped the spacers and I was within specs. As it was before, it seemed just a tiny bit too loose, but whatever. Now that I reassembled it, put new oil in it (the old one did about 1,5k miles), there is no more noise. Diff is silent, all good. I would say the whine was due to too much backlash, however little it was, was apparently out of spec.
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