Actually, if you were to research and do simple searches, it has always been understood to mean AT MINIMUM native birth. Native birth has but one definition.
If we focus solely on the native birth angle, and disregard any parental citizenship, we will find that throughout American history, and indeed in a dozen congressional attempts made since 1970 to amend the Art. II eligibility requirements, it is always, ALWAYS acknowledged that native birth in the US is required.
But then, I have personally spent over 500 hours reading material from the 1790s forward on just this particular topic. Most people don’t commit to such a study.
I appreciate your hard work and your original research.