When doing a Bayesian calculation to find out the posterior for a hypothesis, one does not compare the hypothesis against a particular competing hypothesis; one compares the hypothesis against the entirety of alternative hypotheses.

Yes, but in the case of "the totality of the theories of the mind", this is impossible. You cannot possibly calculate P("poorly conducted, unpublished case studies"| not CT) to get a likelihood ratio. Plus, if you admit more than two competing hypothesis, you lose the additivitiy of log-odds and make the calculations even more complicated.
If you want any hope to get a real Bayesian analysis of CT, the only possible way is to compare it against the best possible alternative.

It appears that you may have a skewed idea of how Bayesian reasoning works.

I think you underestimated my understanding of how Bayesian reasoning works or that I underestimated the inferential distances for Bayesian calculations done in a real case.

So, yes, if the only two hypotheses are CT and FT, and the evidence supports FT more than CT, then it's evidence against CT.

Which is exactly what I said.