look- the "flow" to AA, from PSA, is a gimmick. It exists solely to get people stuck at PSA. American doesn't need it's regional carriers to get pilots. They do, however, need the mainline carrot to sucker people into PSA. The flow is for the regional feed, not the mainline need for pilots.
It's in the contract that you are forbidden to apply directly to American, once you are a PSA pilot.
When (more like "IF") you are able to flow to AA, the primary hiring boom will be long over.
Go to Allegiant, JetBlue, Virgin, or any other carrier with large aircraft if you truly feel stuck and out of options with ExpressJet. DO NOT GO TO PSA.