Yes I have. Twice! BNE to LAX on business with VA. But the good ole days are gone. VA has shut down that door and now AUS to USA direct is almost impossible to book in F or J.
UA will be hard to find as well, generally just 2 weeks out and you might get some sporadic seats.
Qantas is still possible if you look at 11-12 month out and be very flexible on dates. They never release seats on weekend, usually Tues-Thurs. However, if you are using AA or Alaska mile, then I would say you have little chance. AA and AS don’t have access to the award inventory until 330 days out, which is ~1 months behind QFF, Asia miles and BA, so by then almost all seats are taken.
Have you considered Air Canada and be prepared to buy a separate Y ticket to connect to USA? There are up to 3 business class seats on Tuesdays from late Jun next year departing BNE.
Australia to USA is the worst route in the world to find award availability. Even for professionals they have hard time finding award spaces and have recommended that routing through Asia is probably the only viable option (and that’s why AA won’t allow you to route through Asia cuz they know!). But given the current poor exchange rate, unless you already got lots of miles left to burn, buying a revenue ticket might be about the same cost. Eg. EVA business class return to USA is ~ $5000. Worth considering given that their Royal Laurel is almost first class.