MNDOT provides this map

Minnesota Bicycle Maps - Bicycling

It breaks roads down between high traffic or low traffic, and shoulder width. It does NOT show all roads. It shows state and federal roads, and major county roads.

Personal preference, but I would have planned on coming closer to straight south and the turning southeast to get to Minneapolis. I don't know enough to offer information about campgrounds on either route, but the western one would be more remote with less traffic.