It wasn't until 1790 that they passed a law exempting their own children and children of other members of "the club"'s (e.g. children of diplomats stationed abroad) from the strict requirement of US soil birth.
Note that this is NOT a constitutional amendment.
The original Constitution is intact, and still the supreme law of the land.
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’.