Rosemary Garvey's book, "Kilkenny to Murrisk", is probably the most complete history of the Garvey name that is available. According to her account, there were no Garveys holding land in Mayo before about 1575. So Mayo is not an ancient homeland of the Garveys, but rather was a place to which some Garveys migrated during the reign of Queen Elizabeth I. At that time several Garveys acquired land in the area under a redistribution of Church land that was then occurring. The most famous of these was the family of Archbishop John Garvey who had land at Murrisk (civil parish of Oughaval). Relatives of the Archbishop settled at Falduff and Tully (civil parish of Kilgeever). Other Garveys acquired land and built castles at Lehinch, and Lissatava (civil parish of Kilcommon). These places match up approximately with some of the greatest concentrations of Garveys in Mayo in the Griffith Valuation some 275 years later. No settlement by Garveys at Shrule or Drum is mentioned.
The only account given in the book of the origins of the Garveys in Mayo is that most of the ones who settled in the Oughaval-Kilgeever (Murrisk) area had migrated there from the city of Kilkenny. The book claims that they had arrived in Kilkenny less than 100 years before they moved to Mayo. Nothing is known of them before that time - nor is any speculation made as to the origins of the other Garveys in Mayo.
On the other hand.....
The historical account claims that a group of Garveys (O'Gairbhain branch from County Meath) moved into the area of Mayo near Crossmolina in the early 1200's. In that case there would have been Garveys in Mayo about 350 years earlier than the beginnings of the Garveys in Mayo described in Rosemary's book.
This historical account is probably based upon a document written by the Genealogical Office of Ireland in the 1840's called Manuscript 175. As stated in Rosemary Garvey's book, the manuscript was "only as good as the information available at the time". She thinks they got it wrong. Her evidence to the contrary is a document written in 1575 called The Composition of Connacht which listed all the major landholders. The lack of any Garvey landholders in Mayo is taken to indicate that there were no Garveys.
This historical account claims that the Garveys who settled near Crossmolina in the 1200s were a branch of the Garveys called O'Gairbhin. It goes on to state that this Gaelic name would be more accurately translated as Garvin - but was later corrupted to Garvey.
It would be interesting to learn what is known of the origin of the names of the civil parish and townland called Kilgarvan (shown on some maps as Kilgarvey). They are located in the northeast section of Mayo just east of Ardagh and Crossmolina. A place name beginning with "Kil" usually indicated a church or religious settlement.
A detailed account of the life of Archbishop John Garvey can be found in an article by Brian McCabe titled "An Elizabethan Prelate: John Garvey (1527-1595)" (Riocht na Midhe, Vol 9, No 3, pp. 89-101 (1993)). It can ordered at your local library through inter-library loan.