The AA+2 rule (or just 2 other than AA) is firm so I think there's no way around that. Having flown AA & QF, at some point in the itinerary you will have to fly a third OW airline. There also another issue: it seems you have two open-jaws, BNE//Rome and ORD//MIA; I could be wrong on this but I believe you are only allowed one open-jaw .