I purchased 2014 Silverado last spring, 83k miles. What a journey it has been. Did not notice the vibration on test drive. Chevy Shake and 4 cylinder mode shutter. (these are two separate issues). Also rough shifting. I'd like to share what modifications and upgrades I made that worked for me after much research and trips to the dealer.
1. Road Force Balance. $0 by dealer
2. Hydrolic steering bushing $450. 1/2 price by dealer. Helped a little.
3. Custom steel drive shaft $400 installed by me (easy). This made huge difference! Chevy shake all but gone, 90%.
4. Range AFM Disabler. $175. No more 4 cylinder mode. No more shutter. No more burning oil. This is a no brainer.
5. Transmission tune up and inspection . Filter change and flush. $150. No more hard downshift. Still not crazy about the way it shifts overall but both dealers and trans specialist confirmed all normal for this truck, no issue.
Truck drives great now since all above work done last summer. Starting to like it again. I got a great deal on this truck so for me the additional expenses are still under book value.
I hope this helps anyone experiencing same issues and saves you some time.