Bravo for posing problems of science and culture in a coherent manner and in a context such as this. I have just a couple of observations.

1. Though you talk about possible historical birthplaces and future of science, you never define what you mean by ‘science’. Until then, your survey poses only interesting possibilities with no real necessity. I am sure someone from a Judaic, Muslim, or Arabic culture could find similar cross-cultural ties to the birth of modern science. For example, they could claim ‘other’ origins of science to be more pervasive that the commonly accepted Greek origins.
2. But this is the real problem: it assumes that modern science has its origin in Greek science without any argument for this assertion. Leaving aside whether there were Indian origins of modern science, what needs to be clarified first is why Greek science may be — or not – the origin of modern science. In fact, it can be posed and has been posed by many, Koyré, Klein, and Kojeve among others, that pagan Greek science could not have become modern science in the European sense, from Kepler, Copernicus, Galileo, Descartes, and Newton, if it had not been Christianized as a Theological science, i.e., nonpagan science.
3. In anticipation of such clarifications, what needs to be investigated and argued from the beginning is how and why mathematical physics is exemplary of modern science and why this field is not pagan Greek science, but implies a theological foundation. Whether this foundation is exclusively Christian as many scholars seem to think, I defer to argue here. Just to say, many cultures, besides the Greeks, developed a high level of mathematics without extending it to a universal physics. Inversely, like the Greeks, many cultures had philosophies of nature without a mathematization. You seem to imply the latter is the Indian situation when you state, <<Of these, Kaṇāda is the least known. He may not have presented his ideas as mathematical equations, but … >>. Many cultures also made precise computations of the calendar year, the solar system, etc. without this in anyway being a universal mathematical physics in the modern sense of the term.
4. Once this argument is made, then if one is going to suppose that there is such thing as an Indian ‘mathematical physics’ as a forerunner of modern science, then one will have to show why it does not fall under the same critiques of pagan Greek science (who did not have a universal mathematical physics).

Without these clarifications, the letter remains in suffrance.

S