For anything having to do with the Mayflower passengers there is a veritable plethora of information available from the General Society of Mayflower Descendants. They have ambitious projects to document five generations down from every passenger as well as their origins. Many of their works are available in genealogical libraries. You should check what is available for John Billington.
I am a descendant of John Billington. John was that infamous first European executed in the New World for committing murder. The Plymouth Colony did not know the English common law concerning murder, and had to send a delegation to John Winthrop and the Massachusetts Bay Colony to get advice on what to do. This was a bit awkward as the two colonies were not particularly friendly.