Dear Stephen,
You trace the use of math from early astronomy and accounting and along "specific cultural knowledge transfer corridors." And you beautifully mention "hidden interplay of eternal matter and living matter." You observe the efficacy of mathematics in the natural science while noting that humanities and social science lack the cognitive efficiency of methodical math, and thus often get stuck in "endless interpretive linear word chains or quasi-scientific literature."
This is, of course, because counting-based math applies perfectly to the 'eternal matter' or physical universe, while there are no equations which govern the free will of the 'living matter', in which consciousness holds sway. For large numbers of particles, statistics will in most cases suffice, but whether individual or society, the use of statistics on 'living matter' is always conditional, and can never cope with changes occasioned by free will. I'm not optimistic that "a natural science of humanity" is possible, or even convinced that it is desirable. The best we could hope for is probably an economic accounting or optimal resource distribution system, and even this is, as you say, 'tricky'. I touched on some of these issues in my 2014 essay, "The Thermodynamics of Freedom."
I invite you to read my current essay and comment,
Best regards,
Edwin Eugene Klingman