Crojac,
Here's the deal. I've done this four times on American through Santiago to Cordoba. The first ones weren't a problem, but last year American said they couldn't book the guns through to LAN in Santiago. Major disscussion at the check-in in Denver, but we found a smooth way to do it.
When you check-in @ American. Declare your guns. See if they will check them through. If not have them check your regular luggage through to Cordoba and your guns to Santiago. Then have them send LAN in Santiago an intercompany message explaining you will need to get your guns transfered over to your LAN flight. Get a copy of the message to take with you. This will get the guns to Santiago. As soon as you get off the plane in Santiago you will see a LAN help desk in the area where the metal detectors are. "do not go up stairs" Stop at the help desk and tell them you need to make sure your guns will be transferred to your LAN flight. The language thing can be frustrating but they will get the message. Be sure to show them all the documents you have. By doing this, your guns will stay behind security & customs. Be sure to give yourself plenty of time. The American flights from Dallas or Miami arrive approximately 7:00am The morning LAN flight from Santiago to Cordoba is 9:00am. I take the 4:00pm LAN flight just to make sure I have enough time to get the gun situation handled. Just before your flight they will page you "so be sure to hang-out around the gate an hour before the flight" and escourt you to the tarmac for a gun inspection. Be sure to have your Argentina RENAR form, your passport & gun case keys with you when you go for the inspection. The inspectors will be police and in full uniform.
Your return flight shouldn't be a problem. LAN in Cordoba will simply check your guns all the way through to your final destination.
Another thing you need to make sure you have this year is the new resiprocity tax form. In the past you only needed this for entering the country through Buenos Aires. You now need it to enter at any airport. This can only be obtained on-line. The cost is $160.00 and from what I've read, you won't be able to buy it at customs & you will not be allowed to enter the country without it.
Hope this helps. I'll be doing this same drill the end of May myself.
Good Luck,
Paul