My only disagreement is on the # of classes of citizenship.
The case that you cited, Rogers v. Bellei, 401 U.S. 815 (1971) holds the Opinion of the Court, written by Justice Blackmun, that Section 301(a) of the Act, 8 U.S.C. § 1401(a), defines those persons who “shall be nationals and citizens of the United States at birth.”
This means that Congress created a NEW CLASS of CITIZENSHIP, which they designated as “Citizen at Birth” and specified conditions and requirements to retain that citizenship.
This was within their power, but it did NOT redefine “Natural Born Citizen”.
And so 8 USC yes, 8 USC does not redefine ‘natural born’, the problem is, the ‘at birth’ after 1401(a) where the statutes are clear, ‘at birth’ is retroactive upon the parents seeking, filing and receiving it for their child and even then, there are additional requirements the child must fulfill for that citizenship to be perfected. A ‘natural’ born person's citizenship is perfected the moment they are born without the aid of any statute, even without the aid of a birth certificate.
Again, anyone whose citizenship relies on anything past 8 USC, Sec 1401(a), is a naturalized citizen because the US does not have authority to govern the nationality of those born in a foreign country while that person is living in the foreign country of their birth. Justice Scalia covered this quite extensively in one of his lectures last year, how US law has no authority outside the jurisdiction of the US.