“The founders were using Vattel’s definition.”
Not likely since the one understanding was universally known and USED by the Founders in the 1770s, while Vattel’s mistranslation didn’t take place until AFTER the Constitution.
That’s right: “Natural Born Citizen” was not found in ANY translation prior to the US Constitution and was not found in the original French!
From Vattel: “Les Naturels ou indigènes font ceux qui font nés dans le pays de Parens Citoyens.”
And all translations at the time of the Constitution wrote, “The natives, or indigenes...”
It wasn’t until 1797 that an American translation was made that inserted “Natural Born Citizen” for “indigènes”. And remember, indigènes is French for “indigenes”.
Why is it that you want foreigners to be eligible?
That is the opposite of what the founders intended.