OP is unlikely to see his money from CX.

Not to blame OP, but for the benefit of others, given that OP had to claim his luggage at LAX in any event, it only makes a 2-3 minute difference whether the bags are tagged to their domestic destination and thus dropped with AA or one waits the 2-3 minutes at the AA desk to have new tags to PHX placed on the bag.

AA would, of course, apply the bag waiver for Gold/Ruby and not collect the fee.