Trying to set up an artificial crisis in which one outcome is as likely as another is a very bad idea.

If your belief is rationally unjustfiable, a 'crisis' in which one has only a fifty-fifty chance of rejecting the belief is not an improvement in rationality. Such a crisis is nothing more than picking a multiple-choice answer at random -- and with enough arbirarily-chosen options, the chance of getting the *right* one becomes arbitrarily small.

A strategy that actually works is setting your specific beliefs aside and returning to a state of uncertainty, then testing one possibility against the other on down to first principles. Uncertainty != each possibility equally likely.