By the first of November, I would be down around Maryland/DC/Virginia. Better chance of finding open but empty RV parks.
Florida won't be too difficult if you stay north of Orlando or in the center of the state. You can always pick up days here and there in state parks.
Definitely hit the Everglades if you go that far south. The weather is wonderful and, when I was there in January, the campground was pretty empty.
As you head south, you might try Greenbelt Park (NPS) in Greenbelt, MD, about 10 miles from DC. No hookups, but very convenient. Assateague National Seashore is also great in November if you like the beach and don't mind no hookups.
In South Carolina, if you want to visit Charleston, try Buckhall Recreation Area. It has electric and water. The only problem might be getting space.
If you want to visit Savannah, you can stay in the Downtown Visitor Center Parking lot for 2 days for $12.
In Florida, you should be able to get a spot in Anastasia State Park for a few days if you want to visit St. Augustine.
Ocala National Forest has boondocking sites and quite a few campgrounds that should have space.
It sounds like a great trip!
2015 Jeep Willys Wrangler
2014 Fleetwood Bounder 33C
States camped: all but Hawaii
more than 1700 days on the road