Crucial bit of info - Easter weekend. I'd think enough snowbirds have left S FL by that time, either due to end of the month stay expired or due to desire to get back home to spend Easter with family or even tax preparation :( , that you could easily find an overnight slot. Wouldn't have guessed that there were than many Floridians stepping in to take the spots yet.
Anyway, I don't know what size RV you have or whether or not you're self contained. I know of a water front camping spot that has no hookups. I don't think there are published size limitations but I think 30' would be max. Dirt site. $2 per person per night - self pay to a metal box. There are a couple of picnic tables and I see many people fishing there. Within easy walk to a hotel restaurant (closed Mondays) and hotel bar, marina and small marina store. Right on Tamiami Trail about 6 miles east of Collier Seminole SP - Picayune State Forest Preserve. Not on any campground map or app that I've seen. Also know of a place where you could probably boondock without a problem for a night in the same area. PM if you want more info or specific directions. You can see the location of the Picayune site in my signature block - lower middle of the pic.