Just to confirm the APS kiosks are not being used at LAX - at least for we foreigners. It was all queue and be manually processed. It went REASONABLY smoothly when I went through a couple of weeks ago - just long lines but the staff were pretty food. Less shouting than I remember
It probably took me 45 minutes including bag collection and waltz through customs (no more forms and no obvious check) after getting off QF11. Not too bad given some prior experiences being longer (and some shorter back when the Kiosks were in use).
With everything on same ticket booking though I would worry less as you'd be protected by AA I would think so should be fine.
With my situation I took the (I know, don't judge!!) risk of separate bookings and had a 5h break scheduled. In the end I was more than fine as I was out in LAX arrivals area around 8am so had over 3 hours to kill. AA Flagship First check in was really fantastic, including the escort to near front of security line - which I didn't need, but didn't say no to either, also helped a great deal. A really nice OWE perk (I was only flying domestic 2 class"F"). Wound up dozing in QF F lounge for a bit