And this 1790 law says simply that being in a foreign country does not deprive one of legal standing as a citizen in his own country. That’s long been recognized, and long before Blackstone.
So, the principle you mention, “being born of citizens” is preserved. Since being overseas does not deprive one of his rights, then the passing by right and by blood to any children born overseas is preserved.
Therefore, the children born overseas to US citizens are themselves natural born citizens. Stated directly so in the 1790 law and fully in keeping with all other British and American law on the matter.
Blackstone is only authoritative with respect to the meaning of terms in British law. But the term 'natural born citizen' is a term specific to US Constitutional law, and so Blackstone has no competence to speak to its meaning.
As to your other claims, they are comprehensively disproven in the essay I cited.