What you are trying to do requires a bit of work before you call AA ( since you do not want to call them directly) and the advice you got on the aa board is really the most useful.
The easiest way is the join the frequent flyer programs of the respective airlines you hope to fly on and check to see if they show avaliblity. You need not have any miles in the programs and joining is free.
Once you have established the availiblity on the partners (and make sure you indentify some alternatives if your first choice in not available) and have used EF to see U on AA, then call AA.
Personally I believe although the disparity as to whats shown between some programs do exist, but not as great as some make it out to be.
All in all its really not that difficult.
mike