Relighting this thread...........my ZL 1 started to make differential noises at about 3200 miles when turning.
Took it to my dealer and they came up with the following service document:
#PIP5097: ZL1 Rear Differential Moan Noise On Turns - (Mar 6, 2013)
Requires total fluid drain and refill three times with specified driving requirements in between each drain and fill cycle to bring the fluid up to operating temp and scrubbing of the posi-parts. The correct fluid is GM part #88862624 which retails for about $22.00 USD for each 2.43 Qt bottle and several are used. Shop labor would have been over $300.00. Very sweet that it's a freebee under the PIP.
Routine differential fluid change is at 45k miles unless severe service is the case and then it's every 15k miles.
Hope this helps those who are experiencing similar Grannie Groans from the arse end of their ZL1's.
Cheers - Major Boyd