Well, lo and behold, guess what it turns out to be...
A FRIGGIN' BROKEN MOTOR MOUNT!!!
Carlton shot me some photos of what I should look for and it took me less than a minute to identify the busted piece. I have put in a call to the dealership and I will bring it in tomorrow.
The broken piece is so obvious, they must have never looked under the truck. I asked them 3 separate times while I was face to face if they checked it, an was told it was not a broken motor mount. Not a happy customer.