Hi from Australia rootslb. I think I have an ancestor born 1821 whose's family was in Derry, Civil Parish of Meelick in mid to late 1800s, when evicted for non-payment of rent. Some siblings might have lived in Eyrecourt.
I stayed in farmhouse B&B in an adjoining Parish over a decade ago. The guy who owned the farm said he dabbled in local history, had a local book out of print then about Portumna on a table, & was a Catholic. You no doubt realise Eyrecourt district has / has a number of Church of Ireland people, far more than for instance a bit west of Galway City from what I saw. He told me a Parish Priest way back left his worldly possessions to his housekeeper, an illiterate woman. He said the local folklore is the woman didn't realise the value of Parish Registers & burnt them, presumably with other things she considered no value. He told me no point seeing Parish Priest at that time; he was busy doing his job, & nothing survives. On the other hand, I was also interested in Spiddal, when a PP there for decades was also interested in history, & had "retired" due to his age. He had moved into Barna, & was very helpful.
So I use Civil Certificates to find out who was born, married, or died in 2nd half of nineteenth century here. When I visited, I was able to book into the local Registry Office in Galway to look at their registers. But this service was then cancelled after the Global Financial Crisis. They were part of western health department, & around the corner from the hospital. If they have the service available these days, I can give u tips, as time is of the essence.
The Index to BDM for Ireland from the Dublin Office is of course a re-write of forms sent to them from Galway etc, so might have rare transcription errors. But it is online on FamilySearch.org at least.
As I said, I'm an Aussie, just repeating what I've found out or been told; definately not a local, nor an expert. I'd be interested in what u thought of the local area eg the old church & graveyard in Meelick, of Eyrecourt itself [still have new tractors parked in main street?], & there was a Police Barracks on the corner of the road heading south towards Meelick.