The 1790 act demonstrates the original intent of the Framers with respect to the term "natural born citizen". They thought it meant what normal people today think it means: citizen by birth. They had no need to cite obscure Swiss legal experts.
The fact that later laws omit the term "natural born" is irrelevant. The omission of the phrase is understandable, given that "natural born" only pertains to two jobs in the United States.
These same people by and large removed the term natural born citizen from the description and yet retained the term natural born citizen in the Constitution. Please explain why they did this. If, as you feel, they were expressing their original intent as to the meaning of natural born citizenship in 1790, what were they expressing by removing the term in 1795? Isn’t this the crux of the issue? You seem perfectly willing to give them credit for their intent in 1790 yet act like there was no intent in 1795.