I just read thru your query and the follow-ups. Maybe I can be a little helpful. I am recognized by the Mayflower Society as a descendant of William White as well as Isaac Allerton and Richard More. And have been active, with a Wikipedia editor, in creating a Wikipedia page for William White, who previously had none, and for his 2 sons Resolved (my ancestor - who had none) and Peregrine. If I may comment about your posting - in my opinion, the first mistake you made was in taking anything found in Ancestry.com as Gospel. Their sites (Rootsweb. stc.) have as much incorrect information as correct and so does the LDS site FamilySearch. An example I recently found of this kind of stuff was in FamilySearch where they had Resolved White's wife Judith Vassall married also to Pilgrim Edward Winslow (3 postings). Judith was never married to anyone other than Resolved. Edward Winslow was Resolved's step-father but never Judith's husband. And those 3 postings translated to 49 erroneous entries in Ancestry-Rootsweb where the posters had Judith with 2 husbands - Resolved and Edward Winslow! Regarding a few other things in your posting - Elizabeth White could never have been born in Boston in 1609 as no Europeans lived there until 1620 or later with Boston formed in 1630. William White and Susanna _____ (MF says her name is unknown and not Fuller) had 2 sons - Resolved and Peregrine. Susanna married Edward Winslow after White's death and had other children with him. see Wikipedia page: http://en.wikipedia.org/wiki/William_White_(Mayflower_Pilgrimhttp://en.wikipedia.org/wiki/William_White_(Mayflower_Pilgrim)
In my Mayflower Society book for William White Family (Vol 13) on page 58 there is an entry for a William White (Sylvanus 3, Peregrine 2, William 1) who married Elizabeth Cadman. Her parents were George Cadman and Hannah Hathaway. Their daughter Elizabeth White married Benjamin Slocum. That is about about all the Cadmans found in the 5 generation White book.
Hope this might be of some help. If ou wish me to research the White book to a greater extent, let me know. This book is the primary reference for the William White family and descendants for 5 generations out.
Please do not trust internet genealogy if at all possible. I also did when first starting out, but since have developed my own sources and/or did my own document collecting etc.. Not to totally discourage Ancestry research. Their census data where they have photographed old documents is great, but personal genealogy postings are often, at the very best, questionable, with many genealogies being "borrowed" from others with being errors perpetuated.