Your problem, T Hard, is the reason I just joined this forum. I have an '06 C6 with 10,000 miles on it and have the same problem. They changed the oil a month ago and told me I had to drive it a couple hundred miles to get the oil worked into the differential clutches, etc.? I'm blond, so they must have thought I'd actually believe that! I did as told by the mechanic and the noise got worse.......a lot worse. It went from a gentle grinding sound to popping clutches. It's in the shop now getting bearings and clutches replaced as I write this.
What other issues are popping up with my year Vette that I should know about? Is it worth buying the extended warranty or is it a waste of $?