I, um... what? How? I think you've severely underestimated the British and their allies with this alternate version of the War of 1812 here. You had the Native Americans of the Midwest defeated in five months (because apparently killing one guy caused every Indian in the Northwest Territory to stop fighting at once), and didn't even mention the Native Americans south of the Ohio River. The US spent more time and effort fighting their Indian enemies in the War of 1812 than the British at all. And the American Empire doesn't need more land right now. They just got their mitts on Louisiana and Florida. And I can't see an addition of land full of Catholics (who America hates), Indians (who America hates), and Loyalists (who America also hates) as a good idea. Not to mention the fact that the American Empire appears to be unable to lose following the Burning of Columbia.
First off, this isn't 1812 America they are fighting against, these aren't a bunch of unprepared militias who were caught by surprise by a war declaration. This is an America with an actual professional military.
Tecumseh's Confederacy collapsed IOTL after his death, why wouldn't it happen too here ? If you are talking about the Creek War, it will be covered in a separate chapter.
America isn't going to keep all it took, as I said there will be headaches after, especially debates about the Status of Quebec (which America will probably not keep).
There has been only two battles after Columbia, one against an outnumbered enemy in a siege in Montreal, and another one holding the bridgehead of a peninsula against a British assault (and they barely won that if the militia didn't come back).
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