We did the circle tour about 5-6 years ago, going clockwise. Our son goes to college at MTU in Houghton, so we made many trips there taking him to/from school. We made the tour when we dropped him off for his 1st year in late Aug.
Many years we had snow in the UP in the spring when we picked him up at the end of the year - as late as mid-May. Because of that many campgrounds were not open, or if they are, limited facilities (no water or the restrooms were closed) due to snow/cold.
Our circle tour was great. Since we made it after Labor Day, hardly any crowds at all, and still warm. Bugs were not an issue at that time either. My brother did the trip in October, and he ran into CGs closing for end of season.
Our favorite places on our trip - Gooseberry Falls SP in Minn, Sleeping Giant Provincial in Ontario, and Pukaskwa National Park on the North shore in Ontario. But we enjoyed all of our stops.
You do need passport or a enhanced ID to cross the border. Also any pets need documents for vaccinations. At the Soo was the only place we were asked for info on our dogs for all the times we have crossed the border.