So I'm still curious about the DNA results...
I'm thinking that the lack for French ethnicity might be due to a weird roll of the dice in terms of the DNA makeup I inherited from my father and mother. Part of this comes from comparison to a first cousin: we share the Bradish/Guimond side of things but his mother's side of his family is far removed geographically from my father's side of the family. Yet he comes up with 11% French, whereas I come up with 0%. Since the overlap is on my mother's side, I think I can safely preclude any "Jerry Springer"-esque explanation. :-)
So - how to model this? It occurred to me that getting DNA samples from my father and sister (or brother) might be enlightening.
For my father, there should be roughly 50% overlap (from a zeroth-order assumption). So anything that doesn't overlap comes from my mother. If the overlap is far more than 50% (and I'm not a biologist so i don't know if this is a valid hypothesis) then - borrowing from Game of Thrones - "the blood is strong" and genetically, I'm more Irish than French. I'd expect that my father should come out almost exclusively Irish with some English. But for my siblings, I suppose anything is possible in terms of the Irish/English/French ratios (unless my hypothesis is entirely invalid).
In the case of my siblings, they should also have roughly the same 50/50 split (as a base assumption), but with different overlaps. Quantitatively, the difference would be some kind of estimate of the variance within one generation of "shifting" - in other words, "you have your father's nose, but your mother's eyes" might apply to one child, but the opposite for another.
So, if there's X% variance between siblings, then that effect gets multiplied as you go back in time, complicated by the additional consanguine relationships with in-laws with the eventual "genome collapse" that happens when those family lines intersect from a shared common ancestor. (The math for that might be completely impossible to do - but I think it would be a fun challenge!).
I also have to wonder to what extent the rabid genome researchers would love to sample the DNA from these ancestors. Aside from the nasty thought of "grave robbing DNA", it would be extremely interesting and could solve some mysteries. The biggest dead-end on my mother's side is her great-grandmother Célina Boulé: was she adopted? Who are her parents? It's extremely likely that she is also a distant cousin from some blood line, but I think I've successfully ruled out the handful of "possible relationships" that others have used on their family trees.
There's also the intriguing -- though I think unlikely -- possibility that she isn't Québecois at all. Apparently there are cases of Irish children fleeing the potato famine being sent to North America. Perhaps she's one of them - which would also inject Irish ethnicity into what otherwise would've been a nearly 100% French genome, for me only 4 generations back (so 1/16th overall but 1/4 of the Guimond line). If it's also true that she was adopted by Moïse Boulé and Domitille Bernier it might make since since as far as I can tell they had no children of their own.
I have two hopes: 1) that I can get some breakthroughs on my father's side of the family. Finding a few bona-fide third or fourth cousins might open up some avenues; 2) ditto on the Guimond side, in the hopes that eventually we solve Célina's past.