I don't own "Lainhart, Ann Smith. Mayflower Families through Five Generations, Volume 23, Part 1, Family of John Howland, General Society of Mayflower Descendents, Plymouth, MA., 2004," but I searched AmericanAncestors.org, "Mayflower Families Fifth Generation Descendants, 1700-1880," for William Carpenter and he does not appear in the Howland Part 1.
I think the source on the William Carpenter page should be removed, right?