Step One: The AI reveals a personal secret of the Gatekeeper's, which (so far as the Gatekeeper can think it through) could not possibly be known by the AI if it were still safely inside the box.

Step Two: Assorted threats, promises, mindfucks.

(This might not work, since as a Gatekeeper I'd still feel the impulse to respond with "AI DESTROYED", but it's a damn sight scarier than a transparent "I'm already out of the box" bluff. And as for feasibility, I'm willing to believe that an AI making better use of its data than we do could figure out personal secrets that we would think impossible— possibly even ones that I'd think impossible, even given this very belief.)