1. To get home earlier:
Do not fly through Brazil unless you have a visa (assuming you're an American citizen). Also you can fly LAN directly to MIA. LAN also offers several flights via SCL, LIM and UIO then onto MIA. Copa will put you through PTY, Avianca through BOG and AeroMexico (and I believe Mexicana as well) will get you to MEX then onto your final destination (though most likely via MIA). You could also get to SCL via AEP airport in Buenos Aires on Aerolineas Argentinas and LAN if they're telling you that those flights are full. Suerte!! If I'm not mistaken, if you're going through SCL you'll have to pay their reciprocal entry fee you paid when you arrived in EZE (~$120 USD I think?).


2.As far as compensation, you're probably out of luck but writing a complaint sans emotion may reward you 15k miles. Never know... always worth a try as it seems they were at fault at not notifying you that the flight is going to be so delayed! I studied abroad in BA so I can appreciate your frustration getting from the city to EZE!