I have a similar issue now. I have a 2014 crew cab 4x4 with z71 in the V6. I loved my truck until last week. I brought it to Chevy for a recal, well it ended up having three recalls. I also had them calibrate my truck for the bigger tires I put on a few months ago. Well I pick my truck up and now it vibrates in the steering wheel and vibrates a little when you are driving and idling. Dealership says it's normal, but it never did this before I took it in. And they can't fix it and say that's how the v6s are.