Hi Clara,
Have been following this fascinating puzzle with great interest and thought it was about time to toss in a few thoughts, but they probably won't do much to solve the mystery. I missed the earlier posts and have been trying to catch up on the story.
perhaps my grandfather was an Irish orphan (perhaps illegitimate and maybe from Tipperary), who was sent over to Canada as a young boy and brought up by a religious order.
Sorry to disagree, but I don't think this is really very likely.
Many British orphans were sent to Canada, but not to be brought up in orphanages. They were mostly sent to work on farms (particularly the boys). Also the majority were sent by children's homes in England. There were some Irish children sent by RC homes but I don't think there were a great many. I have never heard of any child being sent from a childrens' home and ending up in a similiar establishment in Canada. The whole idea was to get them out of orphanages, out of the city, to start a new life in the wide open spaces of Canada. The reality was sometimes very different from the dream, but that is another story.
If your grandfather was brought up by a religous order, then he was most probably born in Canada or if he was born in Ireland, there is another possibility for how he ended up in Canada and alone: he could have emigrated with parents and they could have died on the voyage or soon after arriving in Canada. I am not sure how bad it was in 1880s, but during the peak period of Irish immigration, thousands of Irish people died at sea or in quarantine after their arrival. There were a great many orphaned children, sometimes too young to know their own names. Families were separated when the sick were sent to the "fever sheds" on an island in the St. Lawrence. Perhaps he really did have two brothers, but had no idea what became of them. Many of these orphaned immigrant children were adopted by other Irish families who had lost their own children. Perhaps your grandfather was adopted and his new family settled in the Ottawa area.
As far as I know, there was no formal adoption, so probably no records.
I have an idea that would explain the references to both the Christian Brothers and the White Fathers. As stated by others above, the Christian Brothers did run schools. The White Fathers did not run schools (for children) or orphanages in Canada.
The Christian Brothers opened a school in Ottawa in 1888.
It was in Lower Town which was largely populated by Irish and French Canadians. Perhaps your gf attended that school. If he was a bright boy, perhaps the good Brothers saw a future for him in the Church. The White Fathers had training schools in Canada (there was one in Montreal) for those entering their order ( I think a sort of seminary with special training for work in African missions).
Since your gf was about 18 or 19 when he ran away, he was old enough to have been in the training school at the time.
Life was probably very hard in those training schools and maybe he could not take it. If he was in Montreal, it would have been easy enough to pick up a job on a ship.
Finally, I must admit that I still tend to think that there is a good possibility that your grandfather was Canadian born and had some Native North American genes, but pictures can be deceptive and I might be wrong.
I hope you find some answers eventually.
Carmela