I am not sure that you are correct about having to know which side of the main channel you are on. Page 52 of the Wisconsin regulation states the following:
Wisconsin – Minnesota Boundary Waters: Applies to the stretch of the Mississippi River shared by Wisconsin and Minnesota lying between the Burlington Northern and Santa Fe railroad tracks on the Wisconsin side of the river and the Chicago, Milwaukee, St Paul, and Pacific railroad tracks on the Minnesota side of the river, including Lake Pepin and Lake St Croix; the St Croix River from the Burlington Northern railroad birdge at Prescott north to the point where the river is no longer a boundary between Wisconsin and Minnesota; and the St Louis River, including St Louis Bay, Allouez Bay, Kimballs Bay, Little Pokegama Bay.
Under the Fishing Restrictions on the Border Waters it states: Wisconsin residents need a Wisconsin fishing license and Minnesota residents need a Minnesota license to fish in these boundary waters. Residents of other states need a nonresident license from Wisconsin or Minnesota. Regulations on these waters may differ between states. You must obey the regulations of the state in which you are fishing.
In my opinion, the critical piece of the Wisconsin regulation is the statement that defines the Wisconsin – Minnesota Boundary waters and then the fishing restriction which states: “You must obey the regulations of the state in which you are fishing.” I interpret this to mean, if you are a Wisconsin resident you follow Wisconsin regulations; if you are a Minnesota resident, you follow Minnesota regulations; and if you are fishing with a non-resident license from a state other than WI or MN, you follow the regulations of the state you bought the non-resident license from. I don’t believe you have to keep track of the main channel or state boundary, that is why they defined the boundary waters, as long as you stay within those boundary waters you can fish following your appropriate state’s regulations. From what I understand there is reciprocity between the states and you can launch from either shore and you can fish anyplace within the defined boundary area.
I could also be completely wrong , but that is how I read the WI regulation.
One side note: If I was from a state other than WI or MN, and I was coming up to fish the border waters exclusively. I would take a moment to review the MN and WI fishing regulations. In my opinion, WI offers you a much more liberal approach to fishing those waters.