I hope you can excuse the direct criticism but that is a very, very poor search outline. By increasing travel dates, origins and destinations one gets an exponential increase in number of possible combinations and then can't do a proper job in searching for availability for any origin XXX and destination YYY.

IMHO you would be much better off understanding the route network available to you with AA awards, picking an origin and destination that are useful to you, expanding the set slightly by adding logical alternates (such as the multiple LAX-area airports if one is headed to SoCal) and running all legal award connections between those points with available search tools: ExpertFlyer, KVS, AA Reservations, etc. Transit time and cost to position shouldn't be dismissed when traveling from 'any' airport.