As you were changing the itinerary/ticketed segments I think that should have been done through AA, noting that QF may not have had an award seat for the BNE-PER flight that you took. Just because there was a seat available does not mean that QF would have had it available on that flight, so QF did do you a favour for getting you on that flight.
Can you ask AA for a refund of the BNE-DRW flight that you did not take or was that considered part of the 80K you paid to get to Australia?
It seems that you voluntarily changed your itinerary, yes it was due to a mechanical disruption, but you had already commenced your ticketed journey and QF offered you an alternative to get you to DRW but you turned it down.
I do not know enough about the current AA programme but I think you may be out of luck.
Also I know from your perspective that is bad customer service but you are dealing with an airline that is not known for its consistent level of customer service.