this is about the only River in Michigan that I can think of piecing together a 7ish day trip, but even that is long for that and you would have seen people, houses, etc. There are damned up sections where you would paddle lake-like sections.
There isn't anything in Michigan that borders or would have put you in the position to really see Canada. I agree with the other poster, sounds like boundary waters, maybe something in Ontario, but I bet you would have remembered crossing the border.
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