Personally I'd price it in coach, pay the difference to a circle pac J fare (which based on your travel plans won't be too much), book through AA flying QF codeshare LAX-SYD on AA flight number, join AA and do a challenge. Platinum by the time you get to aus and you should earn enough points on the trip to pay for a north america - europe return in coach to offset your contribution.

In the realm of sensible answers, in coach I'd likely fly air NZ