Does it by any chance sound like a car backing up with Straight-cut gears?
I have no problem using WD-40 as a light lube and it's always served me well, but I think a heavier grease would be a good idea if that turns out to be the problem.
Does anything in particular make you suspect the rear end?
Might the tires whine only when they're warm or cold? You could raise or lower the pressure a few pounds temporarily and see if it changes the pitch at all.
You might also check for something rubbing on the driveshaft. It's not obvious, but it might happen. Also, is this a manual or auto trans car?
Good Luck
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1990 740 Turbo, on its way to stock specs, maybe beyond
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