I am also amazed that AA do not offer a Flagship lounge at their largest hub – quite bizarre.
I have found previously, travelling either J international or F domestic as a oneworld emerald (so I am not sure which of these factors came into play!) that if you ask nicely it is quite possible to get more than the standard two coupons for premium drinks. I normally ask at the lounge entrance when they are handed out (usually saying something about a lengthy layover or my brain being in a different timezone!). Sometimes they give them to me straight away, sometimes they say I should go to the reception desk inside. Either way it hasn’t been a problem.