Obviously it's hard to improve on anything CWS says, but I had a very similar scenario: in my case the routing was LHR - PHL - EWR on US, booked with an OTA.

I ended up with a seven hour layover when I'd started with a three-hour layover.

I was advised that, despite booking an 'R' fare (a mid-ranking discounted economy on US) the only availability on one leg was in 'Y' (even though there was in fact availability in lower classes). My OTA wanted to help: I really couldn't fault the agent, but the systems weren't there to allow him to do so.

In the end, I managed to call US (via their UK call centre number) and persuaded them to bring the itinerary under their control, which meant that they could see the actual fare bucket availability and gave me flight times that, if anything, were slightly better than the original.

So while I couldn't guarantee that this would work, I'd suggest calling the operating (rather than the issuing) airline and seeing if they can do anything. They may well not be able to - CWS will know far more about the arrangements than me - and see if AA can add a leg on AA stock to the original itinerary.

It may well be that this is a stretch too far, and you will need a supportive and knowledgeable agent in any event, but they do exist. Good luck!