In this scenario, could you possibly see the House of Windsor “going native” instead, becoming an English-Canadian monarch? How would this impact Québec, I wonder? (For that matter, might the Quebec Act then become a basis for removing the exclusion of Catholics from the throne? The “Church of England” would be a moot point, after all...)
Or would be - were it not for its renaming to the Anglican Church of Canada in 1955 from the Church of England in the Dominion of Canada.
As for Québec - it would be interesting. At this point in time, with the particular development of French-Canadian nationalism (which at the time considered itself as wherever French-Canadians clustered together into communities, no matter if in Canada or the US - with Quebec obviously the core of the French-Canadian nation), you still had people who believed the Crown was the best guarantor of French-Canadian rights - much like how Aboriginal people feel about the Crown's role in the treaties. Actually, you had a split in ultramontane French-Canadian nationalism during this period between an older group of nationalists, people like Henri Bourassa, and the circles surrounding Abbé Groulx, who themselves were at odds with liberals like Laurier, so among some nationalists the position of the Crown would be ambiguous. Of course, as far as Québec itself is concerned, the only people who matter when it comes to the impact of Taiwanizing Canada are ordinary Québécois/es, and as Montréal itself is growing from migration from the rural areas (thanks to the United States closing off its borders, thus plugging up New England as the traditional safety valve) that would be part and parcel of their attitudes towards the élites that govern them. In other words, not until the 1950s would that have some impact on ordinary people (if indeed there is a WWII in which Canada is on the side of the Allies).