So decided to take my Z to the dragstrip. Long story short it was a bad idea. I later came to realize that there was something off about when I would go to take off from a complete stop. It basically feels like my shifter wobbles when I go to take off. It feels as though something is loose and the shifter moves along with it. Any idea what it might be?

Motor mount? Taking your car to the strip wasn't necessarily a bad idea, it just might have been the proverbial straw that broke the camel's back. If you lost a mount it was gonna happen eventually, you just sped up it's death, like shooting a zombie bite victim before they turn Back on point I suspect you lost a motor mount or a trans mount, maybe both. Just gotta get it up in the air and check them out.