You’ve both read more on this than I, but the little I’ve seen of Blackstone suggests that ‘natural born’ referred to those who would be classified as citizens by birth, because it is assumed that they would have been born into a natural allegiance to the state, and what has changed over time in the US is who legally would be so classified.
The logic would have gone from ‘if A, then B and if B, then C’ to ‘if A1, then B and if B, then C’.
*shrug*
I've learned a lot from David and Gatún.
But what of the case of a son of a father (or mother) who never was a citizen? In that case I think there is not way for the son to make a proof greater than what will always be the allegiance to his father's (or mother's) country.
That is my read of the extended discussion in Blackstone.
And that is the first nuance.
The second is that the Founder's, clearly did not fully accept the Blackstone/English common law take on "natural born", where it can be read as accepting just the place of birth as a determination in perpetuity. That is, just because children were born in the colonies, prior to the Constitution or the Revolution did not make them forever British subjects. Viz the War of 1812.