Doesn't look like anyone has posted on here in a couple years but I thought I'd share my experience since I rode this solo last August in the event someone else is looking to do it someday. I did a round trip to and from Duluth, MN. I'm from Nebraska so I was fortunate enough to be able to drive up. I made all my camping reservations in advance so I can't speak for the state park issue. I did stay at Tettegouche State Park and it was not full the night I stayed. Here was the itinerary with approximate mileage:
Day 1 - Duluth to Tettegouche State Park (67 miles)
Day 2 - Tettegouche to Grand Marais, MN (62)
Day 3 - Grand Marais to Grand Portage, MN (36)
Day 4 - I took a ferry from Grand Portage to Isle Royale National Park.
Day 5 - Isle Royale to Copper Harbor, MI
Day 6 - Copper Harbor to Hancock, MI (62)
Day 7 - Hancock to Ontonagon, MI (62)
Day 8 - Ontonagon to Ironwood, MI (60)
Day 9 - Ironwood to Washburn, WI (45)
Day 10 - Washburn to Port Wing, WI (35)
Day 11 - Port Wing to Duluth, MN (55)
A couple things to note about the trip....as I mentioned above, I made all reservations in advance except for Port Wing and stayed at either private or municipal campgrounds the whole trip except for a B&B at Port Wing. Regarding the route, the worst stretch in my opinion was from Two Harbors to between Lutsen, MN and Grand Marias, MN. Very narrow shoulders (or nonexistent) on Hwy 61 and traffic can be heavy. I rode that stretch on a Sunday/Monday and would never do that again due to traffic. You'll also come across some logging trucks which can be a little scary. The Gitchi Gami is an alternative but as someone else also said, get your hill legs ready for that. Great scenery on that trail, but very hilly. I rode it for about 20 miles. Grand Marais to Grand Portage is a great stretch of road.
I took a quick overnight in Isle Royale which is worth the trip. The ferry travel can be expensive but they'll transport your bike for a fee. They will either charge you extra for the bike or I got the ferry from Grand Portage to include it in the weight of my luggage which saved me some money. There are no wheeled vehicles allowed on the island but the park rangers allow you to lock your bike up near the ranger station.
The stretch in Michigan and Wisconsin for the most part has good shoulders. Some are a little narrow but generally speaking the traffic was fairly light on those roads. I didn't have much of a problem on those stretches with traffic. Copper Harbor to Ontonagon has some rolling hill stretches so be prepared for that. The climb out of Hancock especially is tough (first 5-10 miles are very challenging)...however, I wouldn't let it discourage you. Scenery is great. I initially had planned on going to Iron River, WI instead of Port Wing but there was road construction. Turned out to be a blessing in disguise. Take Country Road C northwest out of Washburn to Cornucopia and then Highway 13 to Port Wing. Very low traffic and well traveled by cyclists. I met several out on their ride and had coffee with them in Cornucopia. Great ride from Port Wing to Superior, WI (other side of Duluth) but you'll have to go through city streets and neighborhoods to get back over to Duluth. If you can, stay at the Garden House Bed & Breakfast in Port Wing. I made my reservation the night before and it turns out the owners are cycling fanatics so I got treated very well. The Richard Bong bridge from Superior to Duluth has a bike path over the lake that's partitioned off from traffic.
I also worked out an arrangement with the main parking lot company in Duluth and they allowed me to rent a space for one month in a covered parking garage for the time I was gone. If you don't know anyone up there it's a good option.
There's my two cents...highly, highly recommended. Scenery is incredible and take a lot of pictures. Worst stretch is from Two Harbors to north of Lutsen so just ride that on a weekday.