I'm from the North but been camping in Florida since 2005.
Near Everglades City is Collier Seminole State Park. This one is busy. Right now its closed. Keep an eye on it. As we have been tent camping they can always find us room but for a TT you do need to reserve.
Reserve as far ahead as you can. As its close to Naples and golf its a favorite for long stay RVers.. as long as they can get away with it! I am not sure of the length of stay limitations.
There are a couple of nice RV resorts in Everglades City. I have not stayed in either but have parked my truck at Chokoloskee Island Park. Outdoor Resorts in Chokoloskee seems to be nicer.
Flamingo Campground in the Everglades seems never to be full. But there are limited grocery supplies. There is water there is laundry and showers and full hookups at some sites.
There are a couple of campgrounds that seem to be suited for RV's only ( meaning there is little shade!) in Big Cypress
Campgrounds - Big Cypress National Preserve (U.S. National Park Service)
Well, yah you missed all of Nature Coast above Tampa but that deserves another trip. You have enough on your plate now.