LAN is one of the most bipolar airlines around. Their Customer "Service" is routinely an absolute disaster even (especially) for the upper middle elites. I'd guess you're now dealing with the Back Office (Orifice) so you'll continue to get the same kind of response you're getting now. There a couple of ladies that handle the English lines that have always been able to work wonders even when dealing with the BO. PM me if you want their names. I think you're essentially at a dead end with LAN right now but maybe one of the Comodoro Blacks might have a contact in the system somewhere.

Just be happy you weren't dealing with the LIM ground staff during the trip or you'd likely still be waiting to get either a seat, your bags, or even somebody to talk to!