You have everything quite good. William probably left Scotland at 10 for Ireland, at least that is what I think you meant. We havent traced William and Naomi's upline, other than it is said that Naomi is the daughter of Isaac Bates, which you have. We don't have Williams parents.
I would be glad to trade information with you on this line.
I have quite a bit of it in the Clan database, but always need updates. I may already have your line, but you may have some things that I don't. let me know.
Clan MacBean Genealogistwbean@bak.rr.com