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McAlroy (orig. Mac Giolla Rua) has many spelling variations to be aware of including Gilroy and McIlroy.
You may also want to familiarise yourself with all the variations for Freeman as well, especially if the know connection is Mayo.
Sounds like your Freemans probably come from a district on the Mayo-Roscommon border (that shifted in 1898). At the time of marriage Freeman's home farm was in Roscommon but if this place later became part of East Co. Mayo, 20th century family folklore would say it's in Mayo.
Your only link to the parish of Tibohine aka Loughlynn is for McAlroy not Freeman is that correct? Have you any other evidence that Tebocan is Tibohine? There was a RC George McAlroy and Mary Kelly baptising children there in the 1840s. But the records are patchy and no Annie.
Lots of Church of Ireland George McAlroys around Boyle.