I do not know if anything like this.
I agree that "Luke Muehlhauser's work on early-movement growth and field-building comes closest." Animal Ethics' case studies are also helpful for academic fields https://www.animal-ethics.org/establishing-new-field-natural-sciences/
My impression of the academic social movement studies is that a decent chunk is interested in how movements mobilise their resources, recruit, etc, but often more from a theoretical perspective (e.g. why do people do this, given rational choice theory) rather than statistical/empirical. I don't have a comprehensive knowledge by any means though, so could be wrong.
(I generally think that if you have specific questions in mind like this, you have to either draw qualitative, indirect insights from case studies and adjacent materials, or design a systematic/comparative methodology and do the research!)
https://www.socialchangelab.org/ might have some relevant insights here. They've done some work on which factors matter most for protest movements. Though I'm not sure what they're currently working on, or if they have any relevant quantitative estimates and comparisons with other interventions.
Thanks, good shout!
From what I've seen, their work does not quite fit what I am looking for -- they are not comparative and they are also more narrowly focused on left-leaning protest movements, which is more narrow than what I am trying to get at here.