Y-DNA said we were Clandeboy from Moira, County Down. Tickled my daughter, Moira Bridget O'Neal, green to find that out that fact. We were O'Neil (John (1 Culpeper, VA), Henry (2 Cocke Co, TN), Henry (3 Hamilton Co, IL) until !860 Hamilton Census listed Henry 3 as Henry O. Neal.
Hello John,
If I'm reading this right, there's a problem because you've been searching for o'Neals and found one member's last name as O. Neal. Census records can show a variety of ages, spellings, arrival dates, etc., for the same person. So don't rule out Henry O. Neal.
It does seem unusual, though not impossible, that each generation is found in a different state...
I hope this helps.