Each airline has its own Starfile (equivalent). Technically starfiles are specific to Sabre, which used to be AA but was sold and is a separate company but contracts back to AA to provide the reservation service. So there are AA starfiles (and probably the OWE rules are from AA!) and there are other airline starfiles. For the OWE fare there are 8 different files, for each of the Oneworld member airlines (and sometimes they have had different contents!). Sometimes it is very difficult to get any airline to stick to the rules in those starfiles, other times it is trivial. My sense is that you will have a very hard time dealing with AA on this, and probably your L seats will disappear during your fight with AA. So it boils down to how much you want to keep the reservation for the specific dates. Have you determined the fuel surcharge cost from the LAN issued ticket? I suspect it might even be lower than AA, but I don't know.

As for AA having "nothing to complain about" by having GIG-JFK-LHR routing, actually only the JFK-LHR gets AA revenue, and you would be better off not having GIG-JFK on your ticket (AA loses money on that sector for LONEx tickets). If you want a favour from AA, you would have to add NRT-LAX/DFW/JFK to your ticket, so that AA gets the trans-Pacific fare portion as well. Something to consider if you want the "catch more flies with honey rather than vinegar" approach. But the bottom line is that the LONEx product is not really profitable, unlike the DONEx and AONEx products, particularly at the very low ex-Australia price. And, if you really push things, AA can insist that ticketing be done by the airline flying the first sector on your LONEx ticket (which presumably is QF) ... the OW inter-airline agreement does specify that the airline flying the first sector must issue compound tickets (others can issue it at their discretion). Something to consider so you have a complete picture of your rights and privileges in this matter.