Agotta is correct. This is my also my understanding of the discount packages. These were my quotes for identical dates/accomodations/tickets:
Disney pre-code: $1801.24
AAA pre-code: $1623.24
Disney AND AAA with code: $1531.44
So you see, I did get a further discount with AAA (because there was availability), but it is the same quote as the current code with Disney. I think people are getting confused over semantics. Availability is the key, however. If you call AAA and there is currently no availability for the code for your dates/resort, then the AAA TA can't give you a further discount to match. You will need to change something. I think that is what is happening when people say they have called their TAs and were not able to add the code "on top of" a previous booking. Do keep checking back, though, because something (different from the package) that was not available for me one afternoon, turned up available (someone cancelled) the next morning. My guess is there will be new availability for many, 14 days or so out from the day the codes were released (which is the day the deposit is due to hold reservations).
The hint at a dining discount through AAA is something new to the mix and thanks babar41 for checking on that for us!