One thing I learned recently: On-line reservation systems do not show all available campsites at private RV parks and even government-run parks. I made reservations in South Florida for middle to late February this year. I had to wait until mid-November of last year to start reserving when our availability to travel became known.
In at least two cases, the on line booking systems showed no availability, but after calling the parks, the person on the phone was able to find an open slot. I can only speculate that some places hold one or two back from the system, the system is faulty or behind on the availability of sites that come open, or the filters to specify the type of site you need is buggy or poorly designed. On the older system for Texas state parks, the person helping me on the phone suggested I always provide no specifications whatsoever about the type of site I need to be sure I saw what was really available.
In short, call if your computer says they are completely booked.