Once the AAA rooms are sold out, they just sell the regular ones at regular rates. I tried to add a room to our trip this month and they quoted me rack rate since they were out of AAA rooms. You can always check other resorts as the above poster said or just keep calling in case someone cancels.
Can I ask what June code you are waiting for? I thought all the AP and FL resident codes were out past then and there is no way to know if a general code will come out. If you can cancel AAA rooms without a penalty, you may want to get one at that rate(if you can) and then cancel later if a code does come out. Since the AAA rooms seem to go fast, it may be a good idea.