Am I entitled to a full 30 minute lunch break in Kentucky?

They need to allow you to leave your workstation at 6:27 or they're breaking the law. If you're entitled to an unpaid 30 minute break then the time begins when you clock out, not when you begin walking towards the clock. I would suggest you think twice about making an issue of this. Don't bring a knife to a gunfight. Managers have guns.