January 2021 might be possible, but 2020? Regular snowbirds book a year in advance and take most of the favored sites. You might find some a little more inland or less than you would expect for a "resort", but check the reviews at Campground Reviews - Trusted Reviews of Campgrounds & RV Parks. You might get lucky and might have to move a few times.
Making a smooth transition to senility for over 70 years
Have you checked Gulf Shores State Park. If you use their online reservations it always shows full. I usually keep calling (sometimes over a period of weeks) and they always have a cancelation. Also if you are willing to change campsites periodically, you might find something at this "late" date and get a full month in. I absolute love this State Park! Great walking trails, bike trails and I discovered a group of snowbirds who play pickle ball on the tennis courts. AND the Gulf Shores Lodge has 2 lovely new restaurants which are an easy bike ride away.
You might have some luck finding a spot at a mobile home park. We found one last minute in January one year in West Palm Beach. We were about a mile from the beach (and Mar-A-Lago and the Kennedy beach house). Nothing fancy, but full hookups and available, when every campsite was booked out.
Bad decisions make great stories!