There is one last ditched attempt I came across, but couldn't connect the dots to make any true connection, and truly believe only DNA research will help sort it out:
Somewhere many posts ago, Gaffy posted the births/baptisms, and from memory, only John James' stated the McKinstry name, and he was the only one that had a father listed, a fireman.
When Annie lived on Fifth Street, less than a one minute walk from her house (according to Google maps), was a William McKinstry, and his wife and many kids. He was a fireman. He was about 20 years older than Annie, so maybe a much older brother? He was not her father, of that I was sure, but I can't remember why! He was not RC, maybe Methodist. (Sorry, my old notes aren't handy). He and his family lived on Conway Street for years and years. He was born out of county, but must have gone to Belfast as a young man, as he married there.
I went down a lot of rabbit holes with this family, but maybe someone else wants to take a peek at them.