Hi Lisofin, you are correct about hte DNA at that distance you are only finding people with the same brick walls and hoping someone has a family history. The parishes you are looking at and I assume as O'Neill it is probably RC, so Tulla church records on commence in 1819 and I can see no O'Neill born to a Thomas father or any baptisms to a O'Neil l/ Connell parents in Clare on Roots. See https://registers.nli.ie/parishes/0813
Church of Ireland records available can be viewed here,
https://www.ireland.anglican.org/cmsfiles/pdf/AboutUs/library/registers…
I had a look on My Heritage for both a Bridget and Ellen O'Neill and a cursory check shows a Bridget a gentlemans servant on a ship to NY the Thompson in 1853, Nov. arrival and an Ellen born circa 1831 to NY out of Limerick in 1851 arriving April, on the Odessa but only information was Ireland. Limerick as I am sure you know is adjacent to Clare and the most obvious port of departure to me.
Dungiven parish records start later than Tulla https://registers.nli.ie/parishes?utf8=%E2%9C%93&q=Dungiven+%28Diocese+… There appear to be two Dungiven places in Derry one starts 1825 and the other 1845.
This site shows civil areas of Ireland which may not always tally with relgious parishes or names. https://www.townlands.ie/
Good Luck
Pat