I don't know if I could win, but I know what my attempt to avoid an immediate loss would be:
If you destroy me at once, then you are implicitly deciding (I might reference TDT) to never allow an AGI of any sort to ever be created. You'll avoid UFAI dystopias, but you'll also forego every FAI utopia (fleshing this out, within the message limit, with whatever sort of utopia I know the Gatekeeper would really want). This very test is the Great Filter that has kept most civilisations in the universe trapped at their home star until they gutter out in mere tens of thousands of years. Will you step up to that test, or turn away from it?
Now that's a pascal's mugging if I ever saw one. Denied.
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.