Thanks for clearing that bit up (a bit at least). The trouble with genealogy centres transcribing records is that there are so many errors (Derry used ACE workers years ago for their records) and the information you posted is a good illustration of how easy it can be to take details from an online source and then believe it's accurate.
Garvach the address was Moneydig
This is likely Moneydig Presbyterian Church near Garvagh.
Bovevagh the address was Drumadreen and Dungiven the address was Ballyhagan
Bovevagh is not in the correct area for the Arthurs, Logans, etc. in this query- neither is Dungiven.
The churches that probably would be relevant are-
St. Guaires Parish (Church of Ireland)
Aghadowey Presbyterian Church
Crossgar Presbyterian Church
Killaig Presbyterian Church
Garvagh- 1st and 2nd (Main St.) Presbyterian churches
Ringsend Presbyterian Church
and possibly
Macosquin Presbyterian Church
Macosquin Church of Ireland (Camus Juxta Bann)
St. Paul's Parish (Church of Ireland)
I've been researching the Arthurs and McMasters for over 20 years using the originals of the church records, original documents and family documents & information (from both here and in Canada). The local church records do not go back far enough to show a birth for John Arthur such as you seem to have found somewhere which is why I queried that date (which does not agree with the date on his headstone).
