I have found this William and written "could be my guy" on the copy of the census. Maybe a dumb thought, but there is no mother listed here, but wouldn't you guess one of the daughters would have been named Elizabeth if that was the mother's name? I know first and 2nd daughter would have been named after grandmothers, but 3rd boy is named after father, I would guess there should have been an Elizabeth in there. Of course there could have been one and she could have died.
I have found a Wm. Moffatt arriving in New York on 12 Aug. 1851 - another "could be my guy" - but he is arriving with a "Martha" Moffat - sister, wife???
There is also a William Moffat living in Liverpool in the 1851 England Census - born in Scotland - living in Lancashire County, Mount Pleasant sub. reg. district. He is a lodger.
There has just never been any mention of this man having any family before he was married, which makes identifying him so challenging. He had children with his wife Jessie named Elizabeth, Anne, Walter, James and Jessie before his wife Jessie died a couple days after birth of daughter Jessie. The family kind of fell apart after that - one couple took the baby, my G. Grandfather James, 5 when his mother died, went to live with his mother's mother, Anne (Porteous) Thompson. Neither Elizabeth or Anne had children of their own, and Jessie's family hasn't been able to figure out where in Scotland he came from either.
There is a William that arrived in 1856, but with his parents James and Jane, so that isn't my guy either.

There is a William Moffat arriving 19 July 1852 with a Walter Moffat, which would make sense because he names his son Walter later, but this William is listed as 20 in 1852, and my guy should be 23. All these Williams make me crazy. Not sure I will ever figure out this one.
Nancy