A contingent of UEL's settled at Chaleur Bay, (Bonaventure, New Carlisle) Quebec, one of my ancestors, Thomas Rafter settled there. The people who settled there were from a British army unit that had served in either New England or New York state and left the States in 1777. There are documents on line about this group. Also a large number of UELs settled in Eastern Ontario all the way through to Southern Ontario, though in those days it was referred to as Upper Canada. From my research the bulk of UELs had a male family member who had served in the British army and after the Brits lost the American Revolution they came north to Canada which was a British colony. Or it was a family whose husband or father had died in the service of the British army and the family remained loyal to the British crown. I don't know if this helps at all.
as for the Walkers, I wish you well on sorting out the Walkers, I have Walkers on my paternal grandmother's side. They came from northern England in what is now Cumbria (formerly Lancashire). They also had the habit of repeating names in each generation for both the men and the women. Plus the majority of them had large families. My best advice for sorting through the Walker minefield is the more data the better, and birth dates are your best friend. In my case, the most popular male names were Joseph and Nicholas Walker, for the women, Ann, Sarah, Elizabeth, and Agnes. In some genrations, the siblings would repeat the names for their children so there were first cousins who had the same name