Florida state parks have a gate, but if you call and pay for the day, they will leave you an envelope with info and the gate keypad numbers.
Also, if the park is full - many FSP will allow overflow a night in the parking lot. We did that yesterday -- got tired, pulled in, CG full, so they will allow overflow for one night and only if you are self-contained.
Make sure you hit Everglades NP while here -- great place, plenty of sites -- they are never full in Flamingo -- sometimes full in Royal Palms ...