If you plug in the desired dates now and try to book, the site will tell you the date it becomes available for booking. Set your phone up with a reminder for the day before and that date.
The day before, go in and identify the individual sites not yet booked (someone can book the site if their start date is before your start date) and put them in preference order.
On the day, punch in the dates and look at the campground map. Select your top preferred site of those available and book immediately. Have credit card, pass, etc., all at hand before you start. Don't rethink your site priorities.
That's the best you can really do.