And once again, your passage applied to, “children of citizens of the United States that may be born beyond sea, or out of the limits of the United States”. Not to children born inside the country. It has no bearing on this discussion.
I disagree with your opinion, it includes those children of citizens born across the seas or outside the United States if their parents are citizens as natural born citizens in the language of the time.
It also makes the distinction that children with non resident fathers are not citizens. And I humbly submit that English law that defines a King's subject does not apply to citizens of the United States since it is not written into our laws.