That is the nearly the exact same time I am going and I am still playing with my ADRs on a very regular basis! Of course, Coral Reef and Le Cellier have been booked solid for months, but there are still plenty of restaurants with lots of availability (early in the evening too). Definitely try to make ressies at other restaurants. Some suggestions are Marrakesh (our favorite), Nine Dragons (another favorite of ours), and Chefs de France (I just made a ressie here for Sept 22 the other day). Other suggestions: Spoodles (at the Boardwalk), Maya Grill (at Coronado Springs), Plaza Restaurant (at Magic Kindgom), Olivia's (at Old Key West), Raglan Road (at Downtown Disney, I just booked a ressie here last week!). There are lots more, but that should give you a good starting point!
Trust me, you will be able to get PLENTY of reservations if you're willing to be flexible!