I had the dealer put Nitto Terra Grapplers on the truck when I bought it. Mine is the High Country, I oversized the tires to 285/55/20's. They are the same tires, size and brand that I have had on my 2008 LTZ Z71 since I bought it in 2008. They have been great tires.
The wifes new Z71 LTZ has the same vibration at highway speeds. We lifted her truck 3", changed to Fuel Rims and 305 Terra Grapplers when we bought it.
Road Force helped and I think it corrected some of the vibration, I have a 300 mile drive this afternoon and will test it out on that ride.
I do not believe the issue is related to the tires, although it is contributing to the underlying problem. The steering column is just transmitting to much vibration in the hands.
This truck is my 12th chevy truck in my 35 years of driving. I have now bought new 7 chevy pickups an 86, 89, 92, 94, 08 and now 2 2014's. Of all of the new trucks only the 86 4x4 rode rougher than the 2014's.
Is it just me and I am losing my memory or just getting picky as I get older? Or do the new 2014's really ride rougher than the older trucks? My opinion is they do.
My next step will be to check the drive shaft. I am also thinking about getting rid of the stock shocks on the high country.