Hi, Kody!
Been there, done that, too! :-)
At times like these, be creative, patient and persistent. There may still be a way for you to enjoy some spectacular meals, even some with characters, too!
Just to see what is still available, I looked for a table for 4 during your stay. The Crystal Palace has room for 4 at 8:40 p.m. on 11/13/13 and Garden Grove has an 8:00 ADR that night as well. On 11/14, Animal Kingdom's Tusker House has a 2:15 lunch and Disney's Hollywood Studios has a 1:45 lunch as well. On 11/15, Hollywood & Vine shows two dinner openings (4:50 and 6:10). On 11/16, The Crystal Palace has an 8:40 dinner and H & V shows two early dinner options, too. On 11/17, 1900 Park Fare has a 9:40 breakfast and Tusker House has two openings for lunch. Garden Grove also has two openings for dinner.
As Guests change plans, they'll cancel ADRs they made months ago; those ADRs will become available throughout the day, so it's always a good idea to check back in frequently. You might be able to grab one of those openings on the day it becomes available. Either call Disney Dining at (407) WDW-DINE or go onto the website and search for
Walt Disney World Dining Options-Character Dining, using your dates of stay and party size. Think outside of the box, too, by accepting lunch as an option or visiting WDW Resort hotels which offer character dining (some Guests don't realize how easy it is to get to every one of those locations by relying on WDW transportation, so they don't go there.)
Each day, go to the check-in podium at any WDW restaurant and ask the host / hostess if there are any reservations available that day. While there may not be any (weekdays are best), you might have luck snagging an ADR from a Guest who canceled just prior to the 24 hour cancellation window closing.
Hope this helps! Have a WONDERFUL trip!