My '14 Sierra Z71 5.3 with factory 20" wheels also developed the dreaded 72 mph shake at around 17,500 miles. Bought some new tires, didn't completely cure it but improved at first, then, slowly got worse and worse up to 24,000 miles... Had my tires rotated, re-mounted and road-force balanced to .000, thinking that would surely do the trick. No dice. After reading so many articles and posts about the issue online, I solved my problem. Deciding I wasn't going to embark on a mission of back-and-forth to the dealer to try and have them diagnose and cure an obvious systemic design flaw, I traded in the "Black Bueaty" on a new F-150 Platinum 3.5 Ecoboost FX4. Love the new truck and all the technology Ford stuffs into it. Apologies to all you die-hard GM guys but, it's built in Michigan, not Mexico and, so far anyway, it's a fantastic truck. Good luck to those of you still seeking a cure for the bad-vibes. Sincerely.
I'll plan on popping back in from time to time and check on how everyone's making out...
Best regards,
Vance