I am curious, not interested/capable of embarking on such a trip. Is this trip even feasible by canoe or kayak?
The Red River of the North starts along the North Dakota / Minnesota Border, heads into Manitoba, joins the Assiniboine River and flows into Lake Winnipeg. The latter drains into Hudson Bay. So that would be the trip, starting in the USA and heading to Lake Winnipeg. Of course, in Spring, the ‘wrong’ end of the river thaws first, leading to floods. Perhaps the mosquitoes take over subsequently.
Obviously, the border crossing is problematic, but I am just interested in geographic etc. constraints. As high school kids (mid 1950s) we used to canoe each year in the Boundary Waters, paying no attention to border crossings – that has changed. But so have I.