Welp, that didn't help at all. I drove it again tonight and hit the throttle. The car would have crossed the yellow line on my left if I wasn't holding on. So, I let og of the wheel and she tracked fine, hit the gas, slightly, and to the left she went. Let off the gas and to the right she drifted. I recall reading something about this in another Z, so time to search.
'15 3500 HD Dually