The credit card idea is worth trying, although the agent will presumably respond that they have in fact provided the item that the client actually ordered (albeit in error).
But I think it would be worthwhile trying again with the agent directly, if possible with someone more senior than the "front line" customer service people (whose primary mission is probably to make problems go away). I'm assuming that the fare from UK to Melbourne (USA) is less than the fare to Melbourne (Aust). So it would presumably be in the agent's interest to correct the booking and charge the higher fare. I mean, what car dealer would refuse to take back a Ford Fiesta when the customer realised he really wanted the BMW?
I'm sure that if the client ends up having to buy a new ticket to Melbourne (Aust), he/she will not buy it from that particular agent. So what is the advantage to the agent of not helping the customer in this instance?
If all this is explained politely to someone who understands the economics of the situation, it may be fixable.