I think Learning Methods is a more sophisticated rationalist approach than CBT

Interesting. I found the site to be not very helpful, until I hit this page, which strongly suggests that at least one thing people are learning from this training is the practical application of the Mind Projection Fallacy:

Was the movie good or bad? If you answer BOTH, think it through. In a factual sense, can the same movie be good AND bad? If it’s good, how can it be bad? The only way to make sense of a movie being both good and bad is to realize that the goodness and badness does not exist IN the movie, but IN Jack and IN Jill as a reflection of how the movie matches their individual criteria.

The quote is from an article written by an LM student, and some insights from the learning process that helped her overcome her stage fright.

IOW, at least one aspect of LM sounds a bit like "rationality dojo" to me (in the sense that here's an ordinary person with no special interest in rationalism, giving a beautiful (and more detailed than I quoted here) explanation of the Mind Projection Fallacy, based on her practical applications of it in everyday life .

(Bias disclaimer: I might be positively inclined to what I'm reading because some of it resembles or is readily translatable to aspects of my own models. Another article that I'm in the middle of reading, for example, talks about the importance of addressing the origins of nonconsciously-triggered mental and physical reactions, vs. consciously overriding symptoms -- another approach I personally favor.)