Hi, Lauren!
You are going to love the Swan! It is in such a great location and the pool area is awesome. We have stayed there several times and have always been so happy with our choice.
Keep checking on the Coral Reef every week or so. Check online first thing in the morning when the system has "reset" overnight and opens up the reservations that were cancelled the previous day. As you get closer, check more frequently as people change their itineraries around, you might just stumble upon an opening.
I think you might be surprised with getting a table at Cinderella's Royal Table. Since they started requiring a deposit, I find it much easier to get a reservation. If you find that there are no availabilities, check daily starting a few days before your arrival, as guests will cancel to avoid the penalty.
Other great dining locations: Yachtsman in the Yacht Club (next door to your resort!), Whispering Canyon Cafe in Wilderness Lodge, and Cape May Cafe in the Beach Club (also near the Swan). One of my favorite places to eat is right inside the Swan.
Il Mulino is a fantastic Italian restaurant. You can even save by sometimes finding a discount certificate at Restaurant.com.
Have a great vacation, and keep me posted if you get your dining choices. Good luck!