If you have QF Platinum status you can ask QF to clear you on the QF codeshare and almost certainly QF would do that immediately; LA will not, making you wait until a week or so before your flight. If you can tolerate uncertainty (and a non-zero chance of not making the flight for several days) then that is an option. I think it would be cheaper and safer for you to buy another continent and route via NA (the extra FF miles more than pays for the extra fare cost, and you won't have any trouble getting exactly your dates). You can do that using as little as 1 extra segment (out of the 20 seg limit) and would have the benefit of a more comfortable flight on QF and AA (LA in coach is rather poor).