You make good arguments.
Within the Constitution, Congressmen and Senators need to be Citizens.
Only the President must be a Natural Born Citizen.
My belief, the adjective “Natural” before the word Born means something.
Further example > Look to the British North America Act of 1867, to establish Canada. The BNA requires Senators to be Natural Born Subjects (of the Queen). The Adjective Natural meant something back in 1776 and 1876
Yeah, it means not naturalized. Natural born citizens were citizens the moment of their birth, naturalized (”turned natural”) weren’t at the moment of their birth but became it and for almost all things (except being president) are treated as if they were naturally born. It’s really not tough.