You may already have this information. On 30 May 1630 George Minot emigrated (on the William and Mary, it is thought) to New England to join the Dorchester company. In 1897 his descendant Joseph Grafton Minot wrote " A Genealogical Record of the Minot Family in North America." Privately printed. The only hard copy I know of is in the New York Central Library on 5th Avenue. There is also a copy on film in Utah with the Mormons. As I recall it from ten or twelve years ago this listed ancestors trees into Cambridgeshire and Suffolk (UK), as well as the line of descent. No certainty that your Hannah is related to this line, but I wouldn't be surprised. I hope this helps.