Confirmed and significant DNA match to Mahers of Kilcooly

I have a close DNA match to a descendant of Patrick Maher born to Patrick Maher and Bridget Mulhall. Yes, you read that correctly. How much DNA? 145cM across 8 segments, which is a lot. There is absolutely no question that I am related to this individual, and that our MRCA (most recent common ancestor) was probably a great-grandparent or great uncle. We are either second cousins or third cousins.

According to her tree, she is the daughter of a James Hickey and a Johanna Maher. Johanna was the daughter of Patrick Maher and Mary Ryan (these would be her grandparents). She provided some additional clues, enough to go on:  her mother's death date and location, birth date and parents names including her grandmother's death date and location.

Her mother, Johanna Maher, was born in 1915. Johanna's birth record indicates her parents names were Patrick Maher and Mary Ryan and that they lived in Urlingford, Kilcooley, Co. Tipperary. You can see this in the record of Patrick and Mary's first child, Patrick, born in 1914. All of these records are accessible at https://civilrecords.irishgenealogy.ie/

Birth record of Patrick Maher born 1914

The marriage record for Patrick and Mary Ryan indicate that Patrick's father was Patrick Maher.

Marriage record of Patrick Maher and Mary Ryan

They married in 1913, which was only 2 years after the 1911 census, so we should be able to find them in the census, and we do.

Census record Patrick Maher

Census record as listed in database

Patrick has a farm and lives by himself in exactly the same location where he will raise his family. His age tells us he was born around 1867 (the census was conducted in April 1911).

Mary is living in Ballycuddihy (just as the marriage certificate says, and she is a domestic servant)

Census record for Mary Ryan

Census record as listed in the database

So, what about the birth certificate for Patrick?

Patrick Maher's 1868 birth record

You'll see here, in this page from the civil records, last entry a Patrick Maher born to Patrick Maher and Bridget Mulhall. He was born in June.

So, I am related to the son of this family and that is confirmed through DNA. Still how could Ellen 1850 be my great-grandmother, when this couple had another Ellen in 1864?