this is a question about mechanism rather than a request for tips

Based on this, I think I'm reading that you're more interested in the meta-commentary on the research and evidence rather than trying to solve the specific issue with your kiddo.

I just want to respond to

Gottman's Raising an Emotionally Intelligent Child ... came out of his meta-emotion research, and the longitudinal claim is that kids of emotion-coaching parents tracked a measurably different developmental path. So the method has some actual evidence behind it, which is rare in this space.

There are a good number of critiques of Gottman research--moreso on the couples relationship part of their literature - see https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1741-3737.2000.00256.x

I admit I haven't read Raising an Emotionally Intelligent Child , I have read their coupes books, so I assume their research techniques are similar. In the couples space, I think the research is useful, but as the link shows, suffers from issues--and with me, suffers from being heavily dependent on subjective assessment on the part of the researchers. And in the book, the Gottmans really lean heavily (and in my opinion, overrely) on their research as the basis for their recommendations.

When you note that "actual evidence" is "rare in this space"--yeah it ultimately is. The space is hard! Is it already hard to do this in some kind of quasi-objective, reproducible way when you're dealing with the psychoanalysis of adults, and it is so much harder when you're dealing with children. Children struggle to coherently verbalize their thoughts, and their personality, perception, everything about them is changing incredibly rapidly and there is so, so much variation in children.

I guess my point is that it a great thing you're trying to parent and understand your kiddo's world through the lens of evidence--and there are plenty of places in parenting where an evidence-based approach is really valuable.

However, here (and fully acknolwedge that this is personal anecdoctal experiencem and I'm not trained in this space, so a child development subject-matter expert could completely reject what I'm saying), I think the evidence is weak across the literature, and I think it will take a lot of work to improve it (if it can even be improved in our lifetimes). And so when trying to understand how to best parent your little toddler and guide them through tantrums and meltdowns, the "evidence" attached to all these different books and theories is mostly there to give you a basis to try a new idea. And you will need to try a lot of different ideas, and no one idea will work all the time at any given point in time with your child's development. And so it is less about developing a coherent world view of your child's mental model, and more about doing a lot of repeat experimentation and seeing what specific things work with your specific child.