I am also doing some research on the Bachinski name. My father was Thomas Bachinski of Brandon Manitoba and his father was John Bachinski also of Brandon. There were 8 children in my father's family. I just met a first cousin from Winnipeg who was more familar with the Bachinski family.
Please free to e-mail me if this info is of some interest. The Bachinski name (my tribe) was originally Baczynski and the family came from Galicia which was part of the Austro Hungarian Empire at the time, now Poland and Ukraine. They were Polish and Roman Catholic.