This class of citizens is deceased and no longer eligible.
Thus the only class left is "natural born".
The definition at the time was "born in the country of parents(plural) who were also citizens". This definition was quoted in Supreme Court cases, including Minor.
Guess those Justices didn't know what they were talking about either.
Your definition of natural born citizen has no support in case law, nor has any contextual basis in the Constitution.
In fact, there’s many been numerous Presidents who don’t meet your criteria of “natural born citizen.”