Limited Slip Rear End Grinding and Whining

Did you have this condition before the gear oil change? Did you check the axle bearings while you had the rear cover off and gear oil out...if not, don't feel bad...I didn't do it either. Before turning back to the rear end, check for wear and play at your upper and lower control arm bushings as well as making an inspection of the torque boxes where they bolt to the frame...looking for torn or twisted metal or augered out bolt holes. If you are sure nothing external to the rear end is rubbing, worn or broken, I'd suspect an axle bearing. I'd not crack the rear end cover to empty the gear oil until I had the brakes off on the outside chance the noise is pad, caliper or rotor related. When the brakes are off, check for up and down or fore and aft play in the axles...not a great test, but if an axle is worn you may see a preview of coming events at this point. Play or no, dump the oil and pull the axles. Happy hunting!