Yes, it does get a bit flakey the further you go back... (At least part of the flakiness comes from the different meanings of the word "Canada".) In general I would be happy with what you propose.
1) One stylistic comment - I seem to record Canadian counties with "County" as part of the name. I do this because I have no certainty whether there is, or isn't, any possibility for confusion if I
don't use the "County" term. Certainly I have "York township, York
County, Ontario, Canada" - York being a predecessor to Toronto - so I might end up with "York, York, Ontario, Canada" if I didn't use "County" and I seriously dislike internal repeats like that. (My only reason for saying "York
township" rather than "York" was that I wasn't sure whether my source was referring to the settlement (York) or a wider area (York township) ).
(I don't do it for British counties - apart from County Durham - since there is no confusion)
2) Just "Chatham, Kent, Upper Canada" works for me for 1763-1783.
3) For New France,
https://en.wikipedia.org/wiki/Canada_(New_France) has some useful bits - "Canada was the most developed of the five colonies of New France. It was divided into three districts, Québec, Trois-Rivières, and Montreal, each with its own government" might help with subdivisions. I guess these are your 3 areas, so I'd probably use those as county-equivalents....
(For completeness if anyone else is interested, "The other four colonies within New France were Hudson's Bay to the north, Acadia and Newfoundland to the east, and Louisiana far to the south")
I suspect that, back that far, there comes a point when, unless your sources mention them, subdivisions between the settlement and "Canada" don't help a lot.