One group of my Niagara ancestors, who arrived from Pennsylvania thirty years before the US invasions started, did not even speak English. There were a thousand or two others just like them. I don't know how "Brit" they saw themselves but I would guess not very. It wasn't so clear cut and homogenous as you would have it. The War of 1812 started out as a "brothers war" along the Upper Canada frontier and the lines were not clear cut until a series of atrocities were committed (mostly in Upper Canada). You are reciting the Coles Notes version but it wasn't that simple.
Actually you want to read Pierre Berton for the best view of 1812. He cites the following numbers: over half of Canada was of French background and had no interest in joining Anglos in fighting anything. Of the remaining population, one third were Yankee born and came to Upper Canada because land was cheaper and had no problem falling back under the Yankee govt umbrella. Another third of Upper Canada citizens were United Empire Loyalists who were so disgusted at British generals from the American Revolution that they would not fight for Brits again-and or they were Scots and Irish and would not go to the trouble to spit on Brits. The remaining third of Upper Canada citizens were natives-mostly Mohawks who were as disgusted by Brit generals as Empire Loyalists and no more willing to fight.
Berton quotes letters written by Brit commander Isaac Brock wrote home to his family griping about how he hated Canada and how badly he wanted to be back in Europe fighting Napoleon instead of freezing in the true north trying to interest Cdn people in joining his army.
Fortunately for Brock, the remarkable Shawnee Tecumseh forged an alliance with Brits and saved Canada from military occupation. In addition, American atrocities- burning crops and houses persuaded a LOT of Cdns that even though they did not love Brits- they were still better than rampaging Yankees!
One should consider what North America would look like if Tecumseh had lived-his agreement with Brits would have given his people control over a huge territory from the Great Lakes, down the Mississippi to Gulf of Mexico and and east to Appalachian Mountains-with Yankees barred from western expansion by both Brits and a massive native alliance!