Well I can say with my truck it's not the tires. I had some vibration in the right front w/ the stock tires, but now after I lifted and put on 35's it's worse.
I'm the same way, looks like I'm stuck with the "jiggle" until they decide to fix it. Mine is more in the body of the truck and not so much the steering wheel.
Returning member with my '17 Sierra Denali Ultimate in Crimson Red and Cocoa/Dune interior.
Present mods: front tint, WeatherTech in-channel visors, WeatherTech laser/color matched floor mats, Truxedo Duece2 cover and Borla cat-back exhaust.
Future mods: 4" BDS or Fabtech suspension lift, CAI install