Agree with the above as we did some looking at reservations and found none for what we wanted. One way to test the water without dealing with waiting to talk to somebody, is to look at the state parks reservations system. Many now use the same reservation system and it is a bit of a train wreck with so many shifts and changes due to covid but , with some "learning curve" you can drag out the info as well as they can and that lets you play the dates and length of stay to try to get something along the lines of what you want.
But there is also a point to keep in mind in some states where things are not totally shut down but the parks employees are not doing anything in person. Our last trip, we found the rowdies were becoming aware that the ranger, etc. were not doing their normal patrols and things were getting way too out of control in Northern Mississippi COE parks. The pavilions for large crowds were roped off, so the groups were going to the campsites to have group meetings like scouts, weddings, and such.
That left ten cars and thirty people showing up on a site limited to 6-8 but no place to park and nobody to tell them to leave! Since there was nobody at the entrance booth, I had the feeling it was just pretty well open season and we headed back home as we certainly did not want to get into any of the "Karen" situations where we would be the out of towners!