I can give you some info about your potential collateral Murtagh relatives.
My grandfather, James Peter Gallagher, was from Killedan, and his family intermarried with the Murtaghs in that area. Luke Murtagh and Mary Cunnane were the parents of Luke George Murtagh, who was born 14 August 1862 in the townland of Cloondalagh [now Cloondoolough] in Killedan. His sister, Anne Murtagh, was born 17 December 1864, and his brother, Michael Murtagh, was born 2 July 1866 . That Michael iis presumably the one you mentioned in your last message above.
The younger Luke married Mary Gallagher, my grandfather's first cousin, in Killedan in the late 1880's. Mary was from the townland of Carrownteeaun, which is near Cloondalagh. They emigrated shortly thereafter, first to New Jersey, where their first child was born, but then to St. Louis, Missouri, where the rest of their nine children were born. Mary's father, Michael Gallagher, had moved there in the 1870's with the rest of his seven children. The Murtagh and Gallagher descendants are still numerous in the St. Louis area, along with a number of McNicholas and Mulderig relatives from the same part of Mayo. Some of the Murtagh's there use the Murtha form of the name, which is also found in Mayo and in Roscommon to the east.
My branch of the Gallagher family (descended from Michael Gallagher's brother, Peter), including Gallagher's and McNicholas's, ended up in New York, and have many descendants in that area. Michael and Peter had a brother, James, whose descendants remained in Killedan parish. The old family farm is still owned by a relative (in my branch).
Cloondalagh and Carrownteeaun are to the north of Kiltimagh, almost in Bohola parish, whereas Woodfield and Kilkelly are to the east of Kiltimagh. Woodfield is actually in Aghamore parish, to the east of Killedan. and Kilkelly is in the parish of Kilmovee, which adjoins Aghamore. They are both near the parish boundary with Killedan, however. Civil and RC parish boundaries are not always the same, and have changed at times, so perhaps they were once in Killedan parish. In any case, the distances are not great, and people in the area often married people from nearby parishes, so your theory about Patrick and the elder Luke being cousins is entirely plausible, and they might even be brothers (just as their wives, who also share a surname, may be sisters or cousins of one another).
Aghamore has baptismal and marriage records only back to 1864, although there are a few marriage records form the 1820's: https://registers.nli.ie/parishes/1038
Kilmovee has marriage records back to 1824 [with some gaps] and baptismal records back to 1854: https://registers.nli.ie/parishes/0137
All of those parishes adjoin Swinford parish, which has the oldest records in the area [some back to 1808], and I have found that one can sometimes find baptismal and marriage records in Swinford for people living in nearby parishes: https://registers.nli.ie/parishes/0133 Swinford was also the civil registration district for that area, so if you find a civil record for someone in Swinford, that does not necessarily mean that they lived in that parish.
In case you're interested, there were two Irish surnames (from unrelated families) which were both Anglicized as either Murtagh or Murtha. They were the surnames Ó Muircheartaigh ("descendant of the navigator") in Leinster and Mac Muircheartaigh ("son of the navigator") in Roscommon. Actually, there may have been three families, since the name was also found in Scotland, and brought from there to Ulster, where it was usually Anglicized as Murdoch. Either of the two Irish forms of the name could end up as Murtagh or Murtha, depending on how they were heard by whoever was writing out the Anglicized forms (Irish has a number of sounds which English speakers find hard to hear clearly, and there are also regional difference in pronunciation). It was thus not unusual for different Anglicized versions of a surname to be used within the same family. The Murtagh's in eastern Mayo are presumably related to the ones who soriginated in the neighboring county of Roscommon.