You can make reservations to any Florida State Park 11 months in advance for 14 days. The trick is that if you found a park and wanted to make a reservation for Feb. 7-Feb. 21, which is eleven months from tomorrow, you will need to book that in the morning at 8AM eastern time.
The problem is that even if the campground has a bunch of sites available for the selected dates they will get booked within one second of 8:00 AM. Trust me, I just made some of my reservations for Jonathan Dickinson State Park near Jupiter today for Feb. 6th 2022 for 14 days.
It took me over a week to get a site trying every day at 8AM.
Second problem is you are not the only person trying to book the available sites. Hundreds of others want those site too. My advice is be patient and be ready at exactly 8 AM and try to book them quickly. Remember you will have a second or two.
The screenshot you posted shows all sites reserved because they are already taken. There are a couple of single days available but all the days prior to those dates and following those dates are booked already. Just keep trying. How much you try depends on how badly you want to stay there.
We went through the same thing last year when booking state parks in Florida for January and February of this year. Just got home last week.