> He gives a date of c. 1650 with no documentation other than the ballad text itself.

Harvard or not, a major procedural faux pas if he had no external evidence. And if he had, why not give it?

> Assuming the ballad was brought over to the US by the late 1600s seems possible but can't be documented,

Certainly possible, maybe even likely, but beyond that we can't say. Nor do we know how many singers of it there might have been or how widely it was known. The more singers, the more quickly (by 18th C. standards) it may have spread. The fewer, the less quickly.