Calusa sites are privately owned so it will be a sub-lease AFAIK. Maybe the park owns some but you will see a lot of for sale signs. Yes the sites are a little tight and there is a big Latin presence. Key Largo Kampground sites are also privately owed and it was a very nice CG last time we visited. Call first, they are sub-leased. Pennekamp needs to be booked almost a year in advance but if you are a gambler could try a walk up and see if there are any cancellations.
30 miles or so past Key Largo is RV Resort - Tent Camping ? Vacation Activities ? Hotel and Bar | Long Key, FL
Like KL Kampground it was a KOA. We drove through last year to check it out not bad. When going by last month their sign had a $59.95 any site or something like that but call to see, it caught my eye going by but can't swear about the details.
Assuming you mean Sept 5 by 5/9 you may have better luck with reservations than this time of year.