Those are good questions I’m not qualified to answer, however, I believe there is a good deal of work going on in this area. One would need to do a serious amount of background reading of either primary sources or secondary sources that do a truthful assimilation of the best work in this area, before one could really consider whether it were possible to follow this line of research. I am not qualified even to speculate.
But again, simply because I don’t like the answers that I predict may come from a line of enquiry, doesn’t mean the hypotheses, tests or conclusions will necessarily be wrong. This is how we examine reality.
And again, I understand discomfort with following this research process. It risks everything, doesn’t it? Or feels that way.

Explanations in evolutionary biology which teeter on speculation are very different than randomized controlled experiments that seek to establish a model about human behavior. Sociological studies can be difficult to perform at scale with the required control groups, while in particle physics or synthetic chemistry, it can be easier.
I understand that the different methods required for studying human behavior feel fuzzy and down-right unreliable. However, there has been a great deal of development in the research tools and methods that they use as well. Real researchers are not pulling things out of their hats and presenting them as “science.”
Thanks for talking about how you would include philosophy of science in science education. I think you have some very valuable suggestions.
However, I don’t understand how this point would be of value, particularly in a public school – I am thinking again particularly of my New Age coworker, Cathy, as well as my former Hindu, animist, Wicca, generically spiritual, occult-fascinated students would approach this and how that would work in the class:

Explain why claims of supernatural intervention are usually outside of scientific study
You aren’t recommending that we start a study of the effectiveness of charms and spells, prayer, essential oils, etc, etc, etc, are you?
How would such a posture toward science: “claims of supernatural intervention are usually outside of scientific study” help public school students (or any students) better understand how nature operates?
Supernatural intervention may be claimed as a reason, but it is entirely untestable, unrepeatable, unfalsifiable. This is gaps, not an understanding of how the natural world functions.

The number of times I’ve heard someone claim “science has disproven miracles” makes me think category errors should also be addressed.
By whom, and where should it be addressed?
In a public school classroom? By my friend Cathy? She would be more than happy to oblige.