It has taken me a while to get back to you because you asked for a fresh pair of eyes and I'm taking you literally and going back to original records where I can find them.
Your ancestor was known to your family as William and the link to Neil came from some sort of DNA result. So, I focused on what records I could find that is unquestionably your William. A marriage record would be nice but as far as I know, the best that we have is the marriage license notice in the newspaper. I found the abstracted entry for the birth of Archie N. Livingstone that says he was born 7 Nov 1897 but I'm sure that this should have said 1894 because of the next record. The abstract gives the parents names and the father's age and birthplace as 28 and Maine and the mother Annie as 21. Using the corrected date, this places William's birth year as 1865/66. I also had a look at the original image of the 1895 Iowa state census for Lee County, where we find William (29, labourer, Maine), Anna (22, Mo) and Archie (5 months).
We have both looked at the U.S. census of Terraville S.D. where William says that he was born in Canada in May 1865 and that both his parents were born in Scotland.
These are the only records I have seen that give any particulars about William and, to my eyes, they don't suggest that he could be Neil, born in Canada in 1856 to a Scottish-born father and a Canadian-born mother. So, unless this DNA result is a very strong y-DNA match, an by that I mean GD = 0 or 1 at the 37-marker level, I focus on William not Neil.
That being said, I did have a look at baptisms on Mull in the Scottish records site. I did not purchase the images but, assuming that Neil was the individual baptised 11 Mar 1805 in Kilfinichen & Kilvickeon parish on Mull, he had four brothers: Hugh (1809), Alexander (1812), John (1814) and Duncan (1817). Of these sons, only John was listed with Donald and Cirsty's family in the 1841 census and the age doesn't match exactly. Plenty of scope there for other folks connected to Neil to be William's father. The place in Nova Scotia where Neil married is in the coal mining region of Cape Breton Island, just the place where new immigrants from Scotland found labourer work. My own family did the same.
So, this pair of eyes is going to focus on looking further into a William born in 1865, and leave the Scottish connection aside for now.