Dave,
There’s a myth that all Irish genealogical records were destroyed in the 1922 fire. A lot of records were lost but not all. Most pre 1900 wills were lost though there are duplicates, post 1858 for some locations eg those probated in Belfast. A lot of legal and estate papers were lost, the censuses 1821 – 1851 were lost and about half the Church of Ireland’s pre 1881 baptism, marriage & burial records were lost too. However there were no Presbyterian records kept there, nor any other denomination, so the only church records that were lost relate to the Church of Ireland. And even then it’s only about half of their records. The church had instructed that older records be sent to Dublin (ironically for safe keeping) if the local church had no secure place to store them. A lot of churches did have somewhere suitable. It tended to be smaller remoter churches where the records were just kept in the vestry room as opposed to in a safe or vault, that sent them to Dublin. And even then, some of them had duplicate sets. So that’s why Antrim town Church of Ireland, for example, has complete records back to the 1600s, whereas some rural churches nearby do not. They never sent them to Dublin and they remain intact to this day.
You can use Griffiths Valuation to see where the surname Redmond was found in Co Antrim in the mid 1800s. It lists them by parish so you can use that as a basis for further searching in PRONI’s records.
http://www.askaboutireland.ie/griffith-valuation/index.xml
There’s about 50 spread across 10 or 15 parishes.
St Cuthbert’s, Edinburgh, is Church of Scotland ie Presbyterian, so possibly you might want to focus your search in Ireland on that denomination’s records.
Rootsireland and the Ulster Historical Foundation both have some church records for Co. Antrim on-line (they are pay to view/subscription sites), but they don’t have them all by any means. Probably 50%, if that. PRONI has the most complete set. But, as you know, that requires a personal visit. The Presbyterian Historical Society in Belfast also has a pretty complete set of Presbyterian records but they don’t do research and a personal visit is also required to view their records.