3. There are no records of a James Billington traveling from England to the U.S. during that time period, in fact as others mention, there are not even records of Billingtons, or similar names during the needed time period. 4. The story has been handed down through some of the lines the we did come over on the Mayflower. 5.James having a formal education would not have had much of a reason to leave England, and you would indeed need a very strong reason to make that journey.The only thing that might make some since, is if he was closely related to the Mayflower line and had relatives over here, but being separated by over 100 years that doesn't add up either.
I understand we may never be able to prove we are from the Mayflower line, but having did the research in England and turning up no results for a James Billington anywhere in England, anywhere near the time period (1720-1760), I don't see what the other possibilities are.If something could prove 100% otherwise I would be very happy to hear it.
I am going to continue my research as I get the money for it in England, if further searches come up empty, not sure how to proceed.