Bill, Cindy & Alex,
I am a volunteer for Ireland Reaching Out and I live in Co Antrim. I’d be happy to meet you during your trip later this year, provided the dates suit, if you wish.
The information you have provided will be challenging to research. I see trees on Ancestry that place Thomas & Ellen in Ohio by 1844. So they evidently married before April 1845 when statutory marriage registration started in Ireland. Prior to that you are reliant on church records. Not all churches have pre 1845 records and of those that do, not all are on-line. Without some idea of where in Co Antrim the couple lived, it’s the familiar needle in a haystack. (Co Antrim is about 1200 square miles in size. Perhaps 400 churches in the county, at one time. That’s a lot of records.).
Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with FTDNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website).
I did look in the 1901 census for Co Antrim and the majority of Rowleys were Presbyterian, so that may be the denomination to focus on. You probably know anyway but that denomination and Co Antrim origins, point strongly to the family originating in Scotland. They will have moved to Ireland in the 1600s. In north America you tend to call them Scotch-Irish and in Ireland we usually call them Ulster-Scots.