Hey MK! Yes looks like we are cousins. I am in the Chicago area. But my ggg grandfather was a Walter P. Johnston, who received the Medal of Honor at 13 years of age. More on that later. That's an interesting story in itself. Anyway, Walter's mother was Harriet Dillon of Phelps, New York, born around 1820/21. I have that documented. However, when trying to look back further, I came across her name in another genealogy forum as being the daughter of a Thomas A. Dillon, born around 1800 from Ireland and buried in the Old Pioneer Cemetery there. I also have her father's birthplace listed as Ireland as well on a census and death certificate. Thomas was also married to Lucy Spike, who is descended from Edward Fuller of the Mayflower. (So that might mean, and probably does mean, you are a Mayflower descendant as well!) Also there was mention of him being the proprietor of the Vienna House in Phelps. Anyway, this information was on another genealogy forum similar to this (I can send you the link) but was so dated, that I have been unable to contact the person who posted it, nor is it cited with any sources, except one I believe, which is 200 Years of the Town of Phelps by John Parmalee. But not sure if the children's names are what was in the book, or just that Thomas Dillon was the proprietor of the Vienna House. Tonight I just sent off an email to the Phelps Historical Society so we'll see where that takes us.
So basically, I came across the double middle name thing in another book that mentioned him and Lucy having another daughter who married someone by the name of Dickerson. That's where I got my source from of the two middle names. But I, like you, have been on and off with this Thomas Addis Emmet connection ever since. I agree it is a great mystery and one I'd like to get to the bottom of as well as confirming beyond a reasonable doubt that Harriett was one of Thomas and Lucy's children, although I am 99% sure she was based on a few things. Just no hard proof which I need as she is my final connection to the Mayflower Fullers that I need to submit to the Mayflower Society for membership.
I am new here too and I am on ancestry, although my account is lapsed right now. But I do still use it, and you can inbox me through there if you like at cvm4370. Look forward to hearing from you!