Yeah, it's these "different ideas" of contemplative studies that gives it a bad name. There are especially a lot of grifters in the west selling snakeoil "eastern medicine."
Ultimately, you have to try things out and see what affects your subjective experience. You will know by direct experience what is transforming your experience.
If something doesn't work, throw it out.
There are a lot of different ways of meditating, because the brain is complex enough that every person has different predispositions. But ultimately meditation begins by watching your mind so that you can know how it behaves and then testing different things to see how the behavior changes.
But I do like CBT and agree is has the strength you're talking about; it has the rigorousness of scientific research behind it, so its solutions tend to be applicable for larger categories of people.
Science usually throws out anomalies where something only works or doesn't work for a few individuals.