Make sure you do not have checked bags, as I assume you are coming from JFK. At LAX, they will probably be trying to get volunteers upon check-in, and tagging their bags accordingly, so they can be easily pulled off the flight. Unless they are really desparate, they won't want to be retrieving checked bags.
Also, it pays to just get on the list, and be pateient and nice. I once volunteered my seat on SYD-LAX and was awarded an international upgrade certificate..good on any published fare, for the "trouble" of volunteering (they never used my seat).
Let us know what happens!