Generally you will not have too much trouble using a BNE/SYD/MEL to LAX coupon from any of these ports, provided you have re-listed for the appropriate flight. In the event the check-in agent will not accept the coupon, just go see the Ticket Sales desk, who will usually revalidate it with a sticker for that route.

Just remember that technically the answer is "no, you cant use a BNE-LAX coupon for SYD-LAX". However, the rules dont always match real world experience.