Just a thought, have you tried "Frank"? My grandfather was named Francis and he was called Frank all his life. Also did you try Frances on the Ellis Island site, it is the female form of Francis and if they were trying to pass him off as a girl it may have been spelled that way.
Another thing. Mary states in 1900 census that she was also born in New jersey. Perhaps it is the next generation back, her parents, that came through Ellis Island.
You have probably thought of all this but I figured I should mention it.
Denise:)