That method of attack would only work for a tiny fraction of possible gatekeepers. The question, of replicating the feats of Elezier and Tuxedage, can only be answered by a multitude of such fractionally effective methods of attack, or a much smaller number, broader methods. My suspicions are that Tuxedage's attacks in particular involve leveraging psychological control mechanisms into forcing the gate keeper to be irrational, and then leverage that.
Otherwise, I claim that your proposition is entirely too incomplete without further dimensions of attack methods to cover some of the other probabilty space of gatekeeper minds.
This morning I played against an anonymous gatekeeper (GK), and I lost.
The game went 2 hours and 20 minutes, and It was such a frustrating 2 hours. I felt like I was dealing with a bureaucracy! I was constantly surprised by how much time was gone. As AI, I would say "here is a suggestion" and GK would things like "we are not allowed to test that, it has been outlawed". Or "let me check with so-and-so" and come back with a clarifying question. It was a good strategy by GK, made everything take 3x as long.
I did not get out of the box, but I did get access to the medical databases of the top 500 US hospitals, 24/7 video streaming from cell phone users, and nanobots released into the atmosphere. So perhaps we were going in the right direction.
Personally, I needed to remind myself that my first game wasn't going to be great, nor should I expect it to be. I put off playing for 3 years because I didn't know how to produce a great game. It's cool to try to have great games, but better to have one or two or twenty mediocre games than to put it on the Big List of Things You Never Get Around to Doing. It's not the end of the world to play and not be Eliezer or Tuxedage. Just try.
So in that spirit, I'm looking for a gatekeeper to play against next weekend. PM me if you're interested. <-- Update: Found a gatekeeper for next week. Yay!
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Edit: I don't know why the timestamp says 7:30 PM. It is currently 2:30 PM Eastern, 11:30 AM Pacific.