One reason for the lack of results is insufficient detail. And the missing details have to do with memory functions. "Great teachers" first and foremost have to retrieve curricular content automatically and effortlessly. They must read and write rapidly in order to process the necessary paperwork quickly and effortlessly. Only then can working memory have enough space to attend to students. If teaching demands mental effort, the teachers avoid it. So you may find more teacher affects if you collect data on reading speed (silent), arithmetic speed and accuracy, and working memory span.
To get student, the curricula must actually be teaching content with methods and at rates that will enable students to consolidate. But curricular rates are set for the middle class, and the methods are completely empirical. Reading and math fads come and go, but textbooks are set accordingly. There is very little that teachers can do about mitigating bad curricula.
The case of Peru and EGRA illustrates that. Reading completely depends on perceptual learning, and that requires letter-by-letter presentation and a ton of practice to happen. Only then can we talk about comprehension. But textbooks teach whole words and give very little practice. Short of bringing new textbooks in, there is nothing teachers can do to mitigate that.
Many years of educational research by the Bank illustrate one finding: It's impossible to do education without cognitive science. What the donors do is akin to buying a car without an idea what the engine does or whether it will run at all.