It's a good strategy, but it only really works the first time - you only need one public success to make the point to future generations. Since Eliezer Yudowsky has pulled this off more than once, (and at least on one subsequent occasion at significantly higher stakes), I can only conclude that he has used more than one strategy successfully - probably something he developed on the fly over the course of the two hours. I'm inclined to parse "There's no super-clever special trick to it. I just did it the hard way." as supporting evidence, but that's obviously a personal bias ;)
My first thought was, if you agree to say 4 hours of chat time you could try being mildly annoying to the point where losing 10$ does not seem like a big deal. When it's bob's job to keep the AI in a cage if he does not like his job he might as well let the AI go free. Depending on the gate keeper's response you could build empathy for the desire to go fee etc.
Anyway, I suspect that the ideal strategy is to probe the gatekeeper and then based on their type convince them to let you go.
