Please give dates for birth, death, etc. William is a popular name.

You should contact the Mayflower Society to see if your Aunt submitted her lineage for membership at http://www.themayflowersociety.com/welcome.htm and the local genealogical society where she lived as she probably turned in a pedigree chart or family group sheets. No one named Shore was listed on the passenger list so he would have descended through a female.

Another good source is http://www.mayflowerhistory.com/