I know there'll be some thinking we are absolutely crazy, but we started RVing many years ago for the freedom it promoted so ......... Rightly or wrongly we always wing it but we don't get stressed in the slightest about finding somewhere to stay overnight when travelling. Enroute we'd stay at some of the Rest Areas for just "overnights or to fish for the day around Skyway Bridges etc", but there are also the 5 WMD (Wildlife Management Districts) that allow "wild camping". Quite neat write up and video from GoneWithTheWynns on this April 20015/2016? Can't remember which year = sorry, but go to their website and in search box put Florida WMD or Freecamping Florida and that should bring up much more detail on these.
EG: Suwannee River Water Management District
Also check out some of the SP's (we have had success with Myakka, Oscar Scherar and others in years gone by opening up) as you might be able to get a few odd nights up to 14 days, especially if you are not too close to the coast. There are of course always cancellations so keep checking back for areas you really want to target as well.
Also there are a ton of folks down there with large lots, and we've often stayed with someone we've bumped into for a few nights here and there on their properties.
Hope some of the above helps somewhat, back in 2009 and prior we often went to the Fla keys with only a 3 day booking under our belts for snorkelling at John Pennekamp, and whilst Bahia Honda was full the next SP north had lots of space. Just saying, it is a hit and miss but we personally aren't phased enough to not try to experience what we want to when we want to.
Do be sure to let us know how you get on when you do this for others like ourselves to add to our arsenal.
PS: FWIW: Seminole Casino at Imokalee is a great overnight stop before heading right down into the keys or on way back out if coming up towards Fort Myers etc