First argument violates the spirit of the exercise. I would refuse to let someone out unless they had put forth a desperate effort, and that isn't a desperate effort. Second argument... can't see myself valuing several hours of someone else's time anywhere near as much as I value keeping AI in boxes. And any AI worth boxing is smart enough not to generalize from one example.
In general, I think Tuxedage is probably right about emotional manipulation over rational argument being the way to go. With enough epistemic learned helplessness you can freely disregard any argument that you find merely convincing, but it's harder to overcome an effective emotional hack.
First argument looks perfectly within the rules to me.
Second argument is against the rules.
the AI party may not offer to pay the Gatekeeper party $100 after the test if the Gatekeeper frees the AI... nor get someone else to do it, et cetera
Tuxedage and I interpreted this to mean that the AI party couldn't offer things, but could point out real-world consequences beyond their control. Some people on #lesswrong disagreed with the second part.
I agree with Tuxedage and you about emotional hacks.
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.