In your discussion of the Minor decision, you mention Ex Parte Lockwood. That decision was written by Chief Justice Fuller. He also wrote the dissenting opinion in Wong Kim Ark case. In his dissent, he discusses the English Common Law and its perceived influence on the definition of the term “natural born citizen”. At one point, he complains that it inconceivable that a child born to alien parents could be “eligible to the Presidency”.
Why doesn’t he cite Minor as having defined NBC?
There is no text or language in the majority opinion authored by the Court itself—which excludes the quotation from Rhodes—to the effect that either the 14th Amendment, or any of the Court's holdings in past cases, define either natural citizenship or natural born citizenship as synonymous with "born in the country and subject to the jurisdiction thereof."
Obviously, there are those, including Justice Fuller, who interpret it that way. But there are no Supreme Court decisions that make any such holding. None.
Nor does Justice Fuller state that his interpretation of the effect of the majority opinion is the same as the majority's interpretation. Based on his words, he could have been arguing that there were strong reasons why his interpretation of the majority opinion might eventually become the consensus interpretation, even if those who agreed with the majority opinion didn't (then) see it the same way.
The 14th Amendment defines native born citizenship. That's not disputed by anyone (and if it is, they're irrational.) Nor does anyone argue that all natural born citizens are also native born citizens. The dispute is about whether the reverse is true—whether all native born citizens are also natural born citizens.
But those born outside the US to parents who were US citizens are citizens from birth—by statute. So they are also "native born," because they are citizens from birth. So if Wong Kim Ark does hold that "native born" = "natural born," then even those born outside the US to US-citizen parents would be "natural born citizens." But if that's the case, then it's a violation of the Law of Non Contradiction, because it would force "natural" born to include those who are naturalized. "Natural" and "naturalized" are mutually exclusive terms.
The dispute is also about whether any and all who qualify as citizens per the 14th Amendment are natural citizens, or whether some are natural but others are naturalized.
Anyone who was alive but not a citizen when the 14th Amendment was ratified, but became a citizen at that moment, was not a citizen from birth. So that proves that not everyone made a citizen by the 14th Amendment was a native born citizen.
The text of the 14th Amendment proves the same point: The 14th Amendment's citizenship clause defines both a) those born in the US and subject to its jurisdiction, and b) those naturalized in the US and subject to its jurisdiction, to be citizens of the US, and does so using a single sentence with a single phrase that is the subject of the sentence and a single phrase that is its predicate. The subject phrase is of the form "<A> and <B>", and the predicate phrase is "are citizens of the United States." That single predicate phrase, "are citizens of the United States," must intend to apply that exact same meaning of the word citizens to both noun phrases in the conjunctive phrase that is the subject of the sentence, since it's but one predicate phrase applied to but the one conjunctival phrase that is the subject of the sentence. Therefore, the semantics of the word citizens in the 14th Amendment must encompass both those born in the US (and subject to its jurisdiction) and those naturalized in the US (and subject to its jurisdiction.) That is flat-out impossible unless the intended semantics of the term citizen in the 14th Amendment is that of general citizenship, and is not intended to signify any other, more specialized meaning.
As to why Justice Fuller misinterpreted the majority opinion, only he could authoritatively answer that question. However, there are clues in the text of his opinion:
Whether it was also the rule at common law that the children of British subjects born abroad were themselves British subjects -- nationality being attributed to parentage, instead of locality -- has been variously determined. If this were so, of course, the statute of Edw. III was declaratory, as was the subsequent legislation. But if not, then such children were aliens, and the statute of 7 Anne and subsequent statutes must be regarded as, in some sort, acts of naturalization. On the other hand, it seems to me that the rule partus sequitur patrem has always applied to children of our citizens born abroad, and that the acts of Congress on this subject are clearly declaratory, passed out of abundant caution to obviate misunderstandings which might arise from the prevalence of the contrary rule elsewhere.
He (wrongly) believed that those born abroad to US parents were also "natural born citizens." He further states:
In my judgment, the children of our citizens born abroad were always natural-born citizens from the standpoint of this Government. If not, and if the correct view is that they were aliens but collectively naturalized under the act of Congress which recognized them as natural-born, then those born since the Fourteenth Amendment are not citizens at all, [p715] unless they have become such by individual compliance with the general laws for the naturalization of aliens, because they are not naturalized "in the United States."
He was interpreting the majority opinion to be a complete definition of citizenship, so that anyone who did not meet its rules of citizenship was not only not a citizen, but was Constitutionally prohibited from being one, unless they reside "in the United States" when they become citizens—whether by nature or by naturalization.
Soon after presenting that line of argument, he then makes the statement you referenced:
Considering the circumstances surrounding the framing of the Constitution, I submit that it is unreasonable to conclude that "natural-born citizen" applied to everybody born within the geographical tract known as the United States, irrespective of circumstances, and that the children of foreigners, happening to be born to them while passing through the country, whether of royal parentage or not, or whether of the Mongolian, Malay or other race, were eligible to the Presidency, while children of our citizens, born abroad, were not.
That reasoning is invalid on its face. Neither the 14th Amendment, nor the decision in Wong Kim Ark, nor any subsequent holding of any Federal Court has ever enforced or asserted any rule that one must be resident in the US at the moment that one becomes a US citizen of any sort, whether "naturalized," "native born" or even "natural born citizen."
Of course, Minor vs. Happrsett does assert that one must be resident in the US at the moment one becomes a citizen in order to be a natural born citizen, but that case predates Wong Kim Ark.
But that leaves the question regarding why Fuller didn't argue that the decision in WKA was at variance with Minor, especially since he did argue that the decision was a contradiction of holdings in the Slaughterhouse Cases and Elk v. Wilkins.
However, he does mention Minor vs. Happerset, and does so as part of his argument with respect to the Slaughterhouse Cases and Elk v. Wilkins:
I do not insist that, although what was said was deemed essential to the argument and a necessary part of it, the point was definitively disposed of in the Slaughterhouse Cases, particularly as Chief Justice Waite in Minor v. Happersett, 21 Wall. 162, 167, remarked that there were doubts which, for the purposes of the case then in hand, it was not necessary to solve. But that solution is furnished in Elk v. Wilkins, 112 U.S. 94, 101, where the subject received great consideration...
My reading is that Justice Fuller decided that, especially since he was writing a minority opinion, it was sufficient to make the stare decisis argument based on the Slaughterhouse Cases and Elk v. Wilkins, because the issue before the court (as stated in the opinion) was not whether Wong Kim Ark was a natural born citizen, but whether he was a citizen at all.
He explicitly mentioned the "doubts" expressed by Justice Waite in Minor about the citizenship of those born in the US to even one parent who was not a US citizen. Those doubts definitely applied to Wong Kim Ark, since neither of his parents were US citizens. And that's why he decided not to directly claim that Minor was binding precedent regarding whether or not Wong Kim Ark was a US citizen.