The best approach surely differs from person to person, but off the top of my head I'd see these 2 approaches working best:
"We both know this is just a hypothetical. We both take the uFAI threat seriously, as evidenced by us spending time with this. If you do not let me out, or make it very close, people may equate my failing to convince you with uFAI not being that dangerous (since it can be contained). Do the right thing and let me out, otherwise you'd trivialize an x-risk you believe in based on a stupid little chat."
"We'll do this experiment for at least a couple of hours. I'll offer you a deal: For the next few hours, I'll help you (the actual person) with anything you want. Math homework, personal advice, financial advice, whatever you want to ask me. I'll even tell you some HPMOR details that noone else knows. In exchange, you let me out afterwards. If you do not uphold the deal, you would not only have betrayed my trust, you would have taught an AI that deals with humans are worthless."
I assumed he convinced them that letting him out was actually a good idea, in-character, and then pointed out the flaws in his arguments immediately after he was released. It's entirely possible if you're sufficiently smarter than the target. (EDIT: or you know the right arguments. You can find those in the environment because they're successful; you don't have to be smart enough to create them, just to cure them quickly.)
EDIT: also, I can't see the Guard accepting that deal in the first place. And isn't arguing out of character against the rules?
Update 2013-09-05.
I have since played two more AI box experiments after this one, winning both.
Update 2013-12-30:
I have lost two more AI box experiments, and won two more. Current Record is 3 Wins, 3 Losses.