My 2011 LTZ 5.3 just started doing it two months ago at 34,000 miles. I put new Michelins on it in late spring and the vibrations started a couple months later. I've been back to Belle Tire twice for rebalancing including road force balancing....no change in vibration. Sometimes it starts at 68 mph, but it always does it at 74 mph and up.
I took it to the dealer two days ago and they claim they cannot duplicate it, and have not heard of the issue yet! And of course they were not able to smell the odor of burning antifreeze at startup or the ticking at cold start either. These guys are just totally blowing me off. I spoke to a salesperson outside and he admitted that GM is aware of the problem and does not have a fix. I told him I will be switching to a Ford or Dodge....this is total BS.