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Ballybacarrow is in Kilvarnet civil parish. The RC parish is Ballysadare/Kilvarnet but the baptismal records for that parish start in 1842. I did check the subscription site Roots Ireland but the earliest Mary Kearns baptismal record on their data base for Co. Sligo was in the 1840s.
I did check the 1858 Griffiths Valuation head of household listing for Kilvarnet civil parish and there was a Hugh Kearns in Ballynacarrow South possibly a relation to Mary Alice.
I also checked the 1901 census for Ballynacarrow and there were no Kearns living in the townland.
You may want to add Mary Alice's emigration story to our XO Chronicles site and possibly someone will see a connection. https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-data...
Have you considered DNA testing?