According to the Ulster Historical, Foundation website there are 2 graveyards in Glynn parish – Glynn Church of Ireland and Glynn Old. Many Presbyterians were buried in Church of Ireland graveyards so you should consider both. There are very few cemetery records for the 1800s.
I searched the British Newspapers site to see if there was any mention of the funeral arrangements for the 3 Moores you have mentioned. I did not find any. (There is a mention in the Ballymena Weekly Telegraph of 4thDecember 1897 of the sad death of John Moore of Ballyhone, who is perhaps a relative, but perhaps you know about that?).
There are several problems when searching for burials. Firstly, there is no requirement in Ireland to record where someone is buried. Secondly, folk often had family plots in strange places miles away from where they lived (perhaps where their ancestors had lived). Thirdly, Presbyterians don’t routinely keep burial records. Fourthly, only wealthier folk could afford a gravestone in the 1800s. Probably 80% of the population were buried without a gravestone meaning that finding such a grave today is virtually impossible. Your Patrick was a farmer. So that means he would have been slightly better off than the average person, so a gravestone is more likely in his case. But not certain.
Probate abstract:
The Will of Patrick Moore late of Ballyhone County Antrim Farmer deceased who died 24 December 1881 at same place was proved at Belfast by Robert M'William Innkeeper and William Baxter Auctioneer both of Larne in said County the Executors.
The will itself is on-line on the PRONI wills site.
