If you are flexible with days check the CGs recommended Sunday-Thursday. Most people seem limited to weekends. We have been in the area through October before & never had a problem without reservations weekdays. It helps also if you are not fussy about hookups. W/E sites are always easier to get than FHUs. Dry easier still.
Without reservations it is always best to arrive by mid afternoon beating the crowd who are trying to do a 2 week trip in 1 or maybe getting a spot that somebody did a late cancelation on.