I'm trying to present a style of debate which only works if you're actually right. If you follow it and you're wrong, it'll show you that you're wrong in the end.

Basically you say that it's a technique that can be used to identify your own wrong beliefs. How many of your own wrong beliefs have you identified with it?

It is my hope that even the least critical thinkers might adopt the techniques for the sake of "winning," and then find them sufficiently useful that they use them in all discussions, theological or not.

If that's your hope than picking an example that doesn't trigger tribalism would likely improve the chances that a reader engages in critical thinking.