With death in 1901, and living 1 - 2 years in Janesville, w/ daughter...25 years in Evansville...this would put arrival in Rock Co prior to 1875.
I do live in Rock Co, and can go to Mt Olivet and check the headstones for you. They aren't open at the office on Sunday's, but I am familiar w/ the cemetery and should be able to find the stones.
Patrick and Bridget did have a son Michael, who from my memory, died rather young. Could be him that was referred to in the obit that you found.
As for the Evansville paper - they had several old papers in Evansville in circulation for various years. Some overlapped. There is a lady now who is entering obits,etc from those papers, onto the Rock Co, WI site, by name of the person the article featured. They keep those papers on microfilm in the damp basement of the Evansville library, and while they will let people see the things kept there - they require a library staff person to be in the room with you while you look at them. They don't always have the staff to do this...so it's kind of hard to get access to the films.
For some reason, the Hefferan name is familiar to me, but I can't say why.
Still think it's unusual that the funeral would have been at St Pat's in Janesville, unless she was from Janesville, or attended that church. You are correct in that Evansville is NW of Janesville. St Pat's is right in the middle of Janesville. Maybe they lived SE of Evansville, and went to church at St Pat's. St Pat's do have some records - baptisms, marriages, and funeral. They will look them up. If you would like, I can get their address and you could mail them a request for records. The Patrick Ryan family attended St Pat's. Son Daniel operated a funeral home in Janesville, and had the first motorized hearse in town in the early 1900's. He also operated a livery stable with coaches for weddings / funerals prior to motorized vehicles. His son James took over the business, and several of James' sons were involved until their early deaths. After James death, the busines was sold. Sadly, the records are gone. My boyfriend is descended from James / Daniel / Patrick. James widow apparently got rid of all that information after his death. Don't know why. If that had not happened, it would be in family possession now.
Have you gotten any census information on your Ryan's? That should help with where they were born etc.
Tomorrow, I will go to Janesville and drive through the cemetery and let you know what I find.