this sounds like my 87 toyota supra when I didn't put the limited slip diff additive in the rear end. I put the additive from Kragen and never had any issues again

 

Got the friction modifier, put it in, and in less than a HALF BLOCK of driving, it was as quiet as a church mouse. Best part of all, NO WHINE on acceleration or coast. The bluing really helped dial in a good pattern on the gear mesh, and the ring gear threaded bearing adjusters made the rest of the setup a walk in the park! Thanks everyone for all the help.

 

Glad you got her fixed. Not only adding the friction modifier helped, you got the level up to the drain plug probably. Good show!