You can apply AAA rates to your reservation at any time, provided that there are discounted rooms still available.
You can't combine it with any other discount, that I'm aware of.
I just did a quick price check on your resort, and it's slightly cheaper if you book through AAA. However, before you get a AAA membership, is it possible for you to move your package up by one night?
Disney Resorts charge you the same rate from the day you check in. If you check in on the 19th instead of the 20th, you'll be charged the value season rates instead of the MOST expensive holiday season rates.
If you do that, I got a cheaper price through Disney than through AAA.