Excellent summary. As you no doubt know there are volumes and volumes consistant with what you have explained. The Grotian Society Papers - 1972, the Alexander Porter Morse Treatise on Citzenship, the Joseph Story Papers, writings of Grotius, Pufendorf, Chief Justices Marshall and Waite.
I will mention that the 1790 Naturalization Act was repealed by the 1795 Act, eliminating the extension of natural born citizenship to children of citizens born “across the seas”. Mario Apuzzo made a plausible conjecture that this act in 1790 was to extend the “grandfather clause” of Article II to the children of founders; quite a few of the founders spent much time in England and on the Continent. Their allegiance was recognized, but the authors knew the statute would not withstand a test of constitutionality. Today, it is what it was: “...born in the country of citizen parents”.
Today, it is what it was: ...born in the country of citizen parents. BINGO~~~~