Congratulations on a wonderful family photo, some great detective work. and your informative notes and questions.
If I read the 1911 transcriipt of Maria Dillon's baptismal certificate correctly, she was the daughter of Andrew Dillon and Ann Halloran, born on the 5th of June 1844, but the record is not from the Parish of Annaghdown. It is from the parish of Aughrim & Kilconnel in the diocese of Clonfert. That is indeed in County Galway, but quite some distance southeast of Annaghown. There are five or six other parishes in between those two..
Annaghdown is in the Diocese of Tuam and I know those records pretty weit because my GGgrandfather Edmond O'Dea left Annaghdown for the U.S. in 1849. Some of his 7 adult children and 3 grandchildren had preceded him in1848. Annaghdown baptismal records begin in 1834 and I know there were Fords and Cavanaghs living there, but I don't recall seeing Dillons among themand it's a name that would catch my eye because my mother was a Dillon.. You could consult the records for both parishes yourself, because they are online at the National Library of Ireland website at https://www.nli.ie/en/parish-register.aspx.. The record for Maria Dillon's baptism is at https://registers.nli.ie/parishes/0323 (Aughrim, aka Kilconnel) and those for Annaghdown are at https://registers.nli.ie/parishes/1041 (baptisms from 1834, with some marrriages from the 1820s.).
I did some browsing in the original Aughrim records on your behalf and located Maria Dillon's 1844 baptismal record, which is iess formal than the transcript. She was baptized Mary Dillon, daughter of Andy Dillon and Ann Hallorin. Unfortunately, I can't find a way to insert that image here.. But I stumbled across another record in those files that sheds light on your question about connections between the Cavanaghs and the Dillons. Patrick Cavanagh, son of Mat Cavanagh and Mary Dillon was baptized on 5 April 1844, two months before your GGgrandmother was born. His godparents were William Dillon and Mary Dillon. That means that by the middle of 1844, there were at least three Mary Dillons living in Aughrim parish - Mary Dillon Cavanagh and Mrs. William Dillon, both presumably in their twenties or thirties, and the newborn daughter of Andy Dillon and Ann Halloran..
Best of luck in your continuing research, and don't hesitate to hit me up at email@example.com if other questions arise
Edward J. (Ed) O'Day,
Co-genealogist of the O'Dea Clan (USA & Canada)