The Troughton suggestion I believe is nothing but lore. There is no child confirmed that survived after birth according to archive records in England, only a child who died around the age of two. I am not sure how this legend or myth was started, except for the argument that the spelling was changed here in the U.S. after it was recorded or spelled differently by someone else because perhaps the person who brandished the name didn't even know how to write and therefore someone else wrote it down - sort of what happened to some immigrants who came to the u.S. via Ellis Island, New York.
The most plausible explanation is that the first William Trogdon was an only child whose mother remarried shortly around the time of his birth and there is no records discovered so far as to what happened to her husband. There are only two plausible suggestions: He was either a Colonist who came under the Maryland, Charter and died from disease or from some other peril or a Torrey (King's soldier quartered in the colonies), or a Sailor (working on a ship following the slave trade routes). His end is a mystery as is certainty over the spelling of his name and education level.
I see that you have offered another twist in a possible spelling change to the name "Trogdon". Could you e-mail with some details as to how the lore for the third differentiation of a last name change came about. How did you get DNA marking? Is this from an ancestor whose genealogy traces back to Solomon?
On the women's side who married into the Trogdon line there are many extended trees which take me all the way back to the Scottish Kings - Bruce - etc., but none of the British Kings (close, but only the families who were nobility, but not directly linked to one of the Kings of England.) Where do you go to have this DNA testing done and how does one have it compared to these results you are mentioning?
Tim Trogdon, Cleveland, Ohio I am a descendant of Samuel Trogdon.