Limited slip lube WILL NOT affect gear whine. Some ratios are slightly noisy. Many times the pinion shim is reused and the pattern is "good enough". A lot of time can be spent disassembling and reassembling the parts to get it right. I do axles at a GM dealer, GM recomends (even under warantee) if the gear set has been run over 100 miles with the wrong set-up to replace it. I have seldom had to do that. I have had some noisy 83/4 with good patterns. Most of the time around 45 mph with no load.
Doug