how do you know that James was born in 1820? - is this just an estimate or is there some documentary evidence - what other documentary evidence do you have concerning him (eg where + when did he die )

I can't find any bapt for a James Wm or a Wm James Watterson (Manx custom is if 2 forenames then generally known by second)

There was a Mormon Watterson family that emigrated around 1844 see www.manxnotebook.com/mormon/wwatersn.htm was your mother's DNA match to a descendant of this family ?