My 19 3LT A8 Stingray exhibited this at 12k miles -(I bought the car at 10k) dealer couldn't hear, told me it was tire noise, then I took info from this forum to dealer, who performed the left Diff cover replacement - sound went away. Now it's back at 18k miles. Spoke w the dealer today as i was getting new tires (hint they match prices and i printed online quote from wal-mart! - saved me $200) - dealer didn't hear it when they drove and said to allow time w new tires (lol!) - figured i confronted them enough the first time, and I'll give it a few weeks then bring it back with more specific places in local roads to drive and hear it.
Tried taking it to a different dealer with far larger corvette experience, but they stated since dealer#1 did the repair, they have to follow-up.
PS - I have ZERO regrets on buying this model/yr - sorry others do. The only issue I had to date was a bad center console USB plug and new battery required (both under warranty and at different times.) My best fix was spending money with "crazy cowboy" sound deadening which lets me still hear the great exhaust but reduced the road noise and interior bouncing sounds (especially when i have transparent tupperware top on).
If you want to REALLY FALL IN LOVE with the C7 - head out to Spring Mountain, Ron Fellows, and learn just how crazy fast these things go, turns, and stops!! I treated myself a few months ago - not sure they still teach on C7's - but even if "you had to drive one of their C8's" - you'd get the message and be even more impressed with this amazing race car.