As this is a case of first impression, ultimately that is exactly what has to happen. The court needs to make it clear what the founders meant by their use of that particular phrase. Others can and have done the research, but only the Supreme Court can turn it into binding legal precedent.
And with the tendency of the current Court to cite the 14th Amendment and expand rights based on the Equal Protection Clause, I have am positive the Justices would vote include all people born in the United States to not only be citizens but natural born citizens.