I attended a lecture just the other night and the Cleveland/Mayo connection was brought up. Achill/Cleveland corridor had heavy migration 1862-1864 because Cleveland was a transportion hub (Ohio & Erie Canal & RRs). Our lecturer said the current "Flats" section of Cleveland (by the Cuyahoga River) was originally "The Angle" - an Irish area. Lots of the folks went to work as longshoremen. I didn't write the details, but she also said the 3 (?) big towns/areas that came into Cleveland carved out their own spaces - different churches and neightborhoods. There was a great deal of chain migration - 1st family member came, others followed, as did friends and neighbors. By the way, Cleveland & Achill have been "twins cities" since 2003 - still very active. There is also a Mayo Society here and an Irish-American Club (West side) that might be helpful.
I lived in the Ohio City area (near West side) of Cleveland for many years - also an Irish pocket. The church I attended (St Patrick's) was built by Irish workmen who hauled the limestone on horse-drawn wagons from Sandusky, OH (1hr+ by car). The Flats and Ohio City are quite close to each other. One of ther other Irish churches was St Colman and the 3rd may have been St Malachi.