I'd try and find out if your rear has got synthetic lube in it first.
This is my opinion too, but primarily my friends', the one that owned a rearend shop.....
He refused to use synthetic gear lube, said it was too slippery, wouldn't cling to the gears properly. If the customer insisted on synthetic, the warrantee was six minutes or six feet, whichever came first.
He used barrels of Torco Dino oil, exclusively.