Well, I might as well chime in here. Finally. I too have a '14 Silverado (double cab 5.3 LT 3.42 18' Goodyear Wrangler SR-A ) with vibrations/shakes. I want to love this truck. It could be so nice but for the vibrations.
Been watching this thread for almost 3 months but held off while trying to resolve the issue. As far as the "vibration meters" go, every dealer is supposed to have one or was sent one at one time. There is a newer, better one out but not many dealers have it.They are as much witchcraft as science. Having said that, they are not useless though. All that they do is give the tech a frequency and an intensity reading. At no time do they indicate an exact part. It may read "tire 1 or prop 1" or other such things. Tire 1 could be tire, wheel, rotor, drum, axle or any thing spinning at that speed based on the frequency and some math (engine speed,vehicle speed, tire size, gear ratio). So as you can see, it becomes quite involved. A call to TAC is usually required but may have to go higher. After a balance/road force, its up to TAC to lead the way from there. Mine has had 3 road force balances, 2 tires, rear drive shaft sent out and checked, rotors (all) checked for balance. and the dreaded hose clamps on the rear drive shaft. So far very little help. Vibration mostly 40 -50 mph also 65 to 70. Now working with a field engineer but based on our discussion, I'm not holding out a lot of hope. I'll keep trying for a while (2 weeks since talked to field engineer, supposed to be calling/ coming back). Being a tech and customer I don't they can be completely forth coming with me. Good luck to all you vibrators out there. I'll post when I know more.