Campgrounds in Door County and in NF near Ely, MN.

We always stay at Egg Harbor Campground in, where else, Egg Harbor primarily because it has full hookups. They are popular tho so it would be good to have reservations.
Fish Creek Campground on County Road F has space for a 35 footer but, I think, only 30 amp service. No sewers but a honey wagon comes around twice a week to dump your tanks.

One thing to remember is that the state parks (and possibly the other public-land parks) have a 2-week stay limit, so you'd need to move around if you're planning to stay 3 weeks. Some private CGs may have longer-term rates & allow you a 3-week stay.

Bear Head Lake State Park near Ely has been awarded as one of the best in the nation. But - the loops can be narrow with trees and tall brush, making backing a bigger rig challenging. I struggled with my 5th wheel. Best to call them for advice first, and then see what you can reserve.
Fall Lake Campground (NF) is another great spot. A little better for bigger rigs, but again you should spend a bit of time researching then reserving - some say no issue and love it, some say too tight and confining.

Peninsula is a great park, you will need reservations though. If you are persistant and check multiple times a day you can pick up a cancelation (tennison bay or weborg point will work) Wagon wheel is also nice I heard but never been there. Along the way you have 3 state parks to choose from. Harrington beach is big rig friendly, Kholer Andre is nicer but a little tight and Point Beach has something like nine miles of shore line and has some sites that would fit you on the back side. If going through the minacqua area check out firefly Or crystal lake. They might be a bit tight though. We camped at all of them multiple times at different sites and we pull a 34 foot travel trailer ( bumper to hitch) and have had no problems except with crystal and firefly which were a little tight but doable.

Door County & environs are lovely places. We enjoyed camping in their state parks (and Wisconsin has some very nice ones.) That said, they are very popular, and most sites are reservable up to 11 months in advance - something to keep in mind. There are probably a few sites in Peninsula SP where your rig would fit; Potawatomie, however, will be too tight for you, as I remember. There are several private CGs in that area which might work (we never camped in them.)

On your way up there, if you can get a site in Kohler-Andrae SP (near Sheboygan), there are some there that would accommodate you. Nice park - great place to hang out for a few days & enjoy the beach (Lake Michigan), have a meal at the Kohler Resort, or tour the Kohler (plumbing fixtures) HQ. Kohler-Andrae is VERY popular as well; weekdays will likely be more available than weekends, but do check ahead.