My 14 Sierra was in the shop for a whine in the differential on acceleration between 57-60 mph. The backlash was 0.013. The tech tried to shim it and bring the backlash within factory spec of 0.002-0.005 but couldn't get it any closer than 0.008 trying different shim kits. The tech also said the teeth weren't tracking quite right and even the whine wasn't as bad as before, he wasn't satisfied so he ended up changing the ring and pinion and bearings. Preload was set and backlash is 0.004 using the original shims. Now the truck has no whine and is quiet as it should be. I don't know if the preload and backlash wasn't set up correctly from the factory (GM may be lacking in this area) or if the ring and pinion was defective. Whichever, I'm satisfied now.
So then here's the point I want to make. While my truck was being worked on, they let me use a new Sierra SLE with 31 miles on it. I've just recently started keeping up with this thread so when I brought the loner truck back today, I decided to test it on the interstate. When I got around 70-75 shake and bake started! The console was shaking and a WalMart bag I had on the front seat was shaking away! It was awful. There was no comparison in how the loner truck rode compared to mine. As of today, I have had no shakes or vibrations and have driven it up to 85 mph. It's really smooth. The loner truck was a V6 2wd double cab with a 3.23 ratio and my truck is a 5.3 crew with 3.42. So it's just to say it doesn't matter if you have a V6, V8 or what ratio to get the shakes. I've read that drive shafts, shocks, tires, wheels, pinion angles and other things have been blamed with some getting results and some not. I don't know but I'm thinking something in the transmission or transmission area (maybe the transmission cross member like stated in a previous post). Whatever the culprit, I hope it's found and fixed.