I just wanted to give an update on a few things that worked when seeing availability on Expert Flyer that agents or the AS website do not see:
1) Tell them the class of travel you want (O, Z, etc..). The agent at first thought there was no first class availability until I told her this.
2) Ask them to test the legs out separately. Agents are able to price things out without having a leg coming or going from the USA (something you cannot do on the AS website). I was trying to go from HND-DXB and then DXB-LAX. When they tried to put that all in the computer it came back coach for the first leg and first for the second. If you have them try it individually you may get different results.
3) Ask for a supervisor. After the agent contacted the supervisor the availability "magically" appeared.
Just an FYI if you are looking for a May date for DXB-LAX in first check availability for May 5th.