Fuel surcharge is based on the ticketing airline (not the operating one, i.e. actually flying the plane and burning the fuel) ... just goes to show it has nothing to do with a fuel surcharge, but rather a way to collect money. So QF codeshare on AA pays the QF mandated fuel surcharge, while AA codeshare on QF pays the AA mandated fuel surcharge. FF point earning varies based on the fare basis, be careful if crediting AA to QF or QF to AA (some fares earn 0 points, for example).
LAX customs isn't a problem for the SYD flights if they are on schedule, as they clear in T4 and not in TBIT (the other flights are in TBIT though which is problematic at that time of day). Also QF has a much bigger presence at LAX (not that this seems to have helped any with their last few irregular ops; but in theory they should be better able to deal with problems at LAX than at SFO).
The primary benefit of the AA challenge is that you would have QP access for a year or 2, however you would have to plan it carefully as you might not have enough points to qualify on discount fares, or have to book AA codeshare trans-pacific (generally a few hundred dollars more than QF on the same plane, but not always). It doesn't sound like you do enough travel to make the lounge access worthwhile.