I would like to report an encouraging development. I took my 2014 Z71 double cab into the dealership about two months ago to get the vibration problem looked at. They told me I had one tire out of balance which they said they rebalanced. Afterwards, I took it out on the highway but still had a slight vibration at 70-75. After reading all the post on this forum, I decided just to wait and see what happens. Well, over the last month or so, the vibration has completely stopped. 75 is smooth. Took it up to 85 yesterday. Still smooth as glass. I just turned over 3200 miles. I have no idea why the vibration has stopped. Tire wear, suspension breaking in, what??? Whatever has happened, I hope it is permanent.
As a side note, I have not experienced any other problems some folks have been reporting. No noise in rear end, dash is not warping, no rattles. This is the third Silverado in a row I have owned. I had a 2004, 08, now a 14. This truck is the best by far. It's tight, quiet, the 5.3 is kick ass and all electronics to include mylink works perfectly. I love this truck...as long as the vibration issue remains a non-issue.