Wes, while I do see your argument. I respectfully disagree. In the time of the founders, such cross-border travel was immensely difficult. It took at least months to sail from Europe to the United States and it would mean enduring great risks. Also, women didn't know they were pregnant as early we do now. Such a journey may be impossible to finish on time.
Also, the Founders were concerned with those who had special titles. They did not want a special group with special titles (duke, earl, etc.) to essentially lord over the rest of us. This may be a place where the Constitution is anachronistic. This is similar to the fact the Founders could not talk about searching a computer or its data in the constitution. Such things did not exist.
Going down a route that the founders probably meant "born to US citizens" rather than "natural born" is a dangerous rewrite when the Founders could have said the Former.
This is pretty much settled law though now.