I believe my link (pg 888-889) show the founders did not share your view of natural born citizenship. Furthermore, there is evidence that at least one former US president (Chester Arthur) was born of one non-US citizen.
OK, I read those two pages. They say that they don't say.
I.e., they say that neither Jay's nor Hamilton's correspondence are specific about the matter of what exactly constitutes a "natural born citizen." And they say that correctly, because the excerpts this book lists are not definitive on the matter.
Therefore, one must look at the contempraneous sources that these founder and framer folk frequented -- and the documentation of others. That is what I have just given you. ;-)
Now, the significant point is that Jay sought to exclude foreign allegiances for the Commander in Chief, in requiring a "natural born citizen" -- something that Donofrio is explicit about in his suit.