We will also be in FL January and February. I started reserving sites around June. Luckily, most of the places we want to visit are in the Northern half of the state - the further south you go, the harder sites are to find. Sites are much easier to get inland than on the coast. They are also easier to find with shorter rigs - the long sites are booked quickly.
Everglades, Ocala, and Fort Pickens (Federal) are pretty easy to get walk in sites. It is pretty easy to get good sites on the panhandle during Jan-Mar as it tends to be colder.
The only thing I can suggest is to do what I have been doing - pick your spots and check every day for cancellations. I picked up two weeks at Gamble Rogers (on the beach) that way.
We tried last year to just wing it and did manage to stay at some place or another for a total of six weeks. But in some campgrounds we could only get a day or two; we moved a lot.