I looked at D4YouFly via the Air Control app and you would be fine. That's a Brevard County park and I recall seeing No-Drone signs in those parks years ago but I think they have rescinded those. Best bet is to just call and ask: (321) 264-5037
Interesting that the statute prevents any filming of public & private schools. I have no interest in doing so but could easily see myself inadvertently capturing one nearby to a community I'm filming.
My guess is they are more worried about the Chinese having access to the drone than they are about domestic terrorisms. Clearly misplaced in this case.