Let me give you some hard information on how to interpret "natural born citizen" in Article 1.
This is a page from a Pennsylvania Law book published in 1817, and is described as being based on the report of the entire Pennsylvania Supreme court in 1808.
Philadelphia was the site of the Constitutional convention, and many of the judges on the Pennsylvania supreme court were participants in the process of creating and ratifying the US constitution.
These judges know better than anyone what was meant by "natural born citizen".
A Digest of Select British Statutes comprising those which According to the Report of the Judges of the Supreme Court, made to the legislature, appear to be in force, in Pennsylvania, with some others, with notes and illustrations.
by Roberts, Samuel, 1763-1820; Great Britain. Laws, etc; Pennsylvania. Supreme Court
https://archive.org/details/digestofselectbr00robe