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This is for a TL I'm working on. I know there are plenty of threads on this forum about British gains in the War of 1812, but I haven't noticed a lot of threads about this specific topic. What could have led to the cession of Michigan's Upper Peninsula back to British control in the terms of the Treaty of Ghent?

From my understanding, the British didn't commit as forcefully to North America in the conflict due to the Napoleonic Wars. What I'd prefer for this scenario is for there to be no major long term changes in Europe because I want to minimize the butterfly effect there.

Is a more forceful British campaign in Lower Canada realistic considering the conditions of the European front? Could their annexation of the UP (or any part of the NW Territory) be considered a realistic option without greatly affecting the course of the Sixth and Seventh Coalition Wars?
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