[MandK]

If you could live with being about an hour north of Jacksonville, you could try Coastal Georgia RV park. We are staying there during that time period for a couple of days on our way to FL. When I booked it last month they said they had plenty of room, but of course that was then. If you can get in and then work out something better in the meantime, they advertise a cancellation 3 days before arrival gets you your deposit back less $5.
I have never stayed there before and know nothing about the park but it looks nice and very convenient to the interstate, just throwing it out there. Good luck.