Tom, my pleasure. Seems we have turned over some of the same stones in our research, so it's good to compare notes.
Starting from the Bridget Keane angle, I note that the three counties where the name Bridget Keane occurs are also three of the four counties where Keane is most common (the other being Clare). I am inclined to think that these are three separate women. But I leave that to your judgement.
Indeed, I have another Bridget Keane. I think that the John & Bridget Keane (nee Jennings) from Kiltullagh parish Co Roscommon are not the same couple as yours. Their children were mostly baptised in Kiltullagh parish 1851-1872, but there was a gap of several years. I searched Tuam parish registers during those gap years and found a Patrick Cain baptised 1864 to John Cain & Bridget Jennings. The family believed their Patrick was born 21 March 1858 so it's not a straight fit for them, or for your family either, seeing they had a Patrick b. 1872.
We have one other useful clue, the Y-DNA of their USA descendant, whose Y-DNA matches my family. We had a common ancestor about the time of cromwell, which might explain how/why we ended up dispersed over two counties in Galway & Roscommon.
If your Y-DNA is a sample I see in the Cain DNA project, then the John Keane & Bridget Jennings of Kiltullagh are not related to you. Their names remain quite a coincidence though.
The Patrick baptised 1864 at Tuam could conceivably have been from your family, and perhaps died young before Patrick born 1872 was named after him?
The other Keane family who appear to fit better descend from a John Richard Keane, born ca 1848 to John Keane & Bridget Jennings, reportedly of Tuam, Co Galway. He had a son and a grandson named Ulich (spelling varies, sometimes also Ulck, Eulich). I am inclined to think that he is an elder son of your John & Bridget. Male line descendants survive but I have yet to persuade any of them to provide a Y-DNA sample, which would settle the relationship one way or the other.