Examining where our first destination airport may be... (Quick summary at bottom of post!)
We know teams were on AA 276, LAX-MIA (26/11 2255-0640). Connecting through Miami suggests Latin America, so we'll start our investigation there. I believe Central American countries have better direct routes from LAX, so I'll be leaving them aside for now.
Let's start with Sao Paulo, the biggest airport in South America. There's one flight leaving Miami at 9.00am, but it's a TAM/United/Continental codeshare, which makes it an unlikely connection for our teams just getting of an AA flight, on a competing airline alliance. The next flight down to Brazil isn't until 6.15pm, so I'd doubt our first destination is in Brazil.
Miami has flights to Santiago, but the first flight that teams can catch leaves at 8.20pm, 13 hours after they arrive. Doesn't sound like a very feasible itinerary for TPTB to arrange.
Next up, Lima. The first available flight leaves Miami at 3.15pm, which is pretty late. However, it's a TACA flight, which is on an opposite alliance from AA. The next flight out is an American Airlines route, but it leaves Miami at 6.30pm, arriving at 10.05pm. Compare that to the direct LAX-LIM flight, which leaves two hours before the LAX-MIA flight but arrives at 7.45am, making a whopping 14 hour difference between lead teams and trailing teams. Not too possible then?
There's an AA flight from Miami to Caracas, but I don't see any other good ways to get to Caracas from Los Angeles that arrive at a similar time. The route to the Guyanas is so complex if you try to go through Miami that I don't think TPTB would bother.
The two flights from Miami to Quito arrive at 6.10pm and 7.05pm. No other alternative routes into Quito. It's still a possibility, but all teams would have to be on the same flight from Los Angeles to Miami, making it kind of anti-climatic. The start would probably have been Miami instead.
The only flight from Miami to La Paz leaves too early for our teams to catch, and the connections through Lima don't make sense at our timings either. Other airports in Bolivia are even harder to get to.
There are flights from LAX via Miami to Bogota, with teams switching from AA to LAN, both Oneworld members. Other possible flights from LAX include connections in Mexico City, San Jose, and New York. Colombia is not ruled out by this investigation, although I'm not too sure TPTB would hold a leg there. Asuncion and Montevideo are possibilities, but they require connections through Sao Paulo or Buenos Aires. This adds a whole new level of complexity that I'm not ready to handle just yet.
Which leaves Argentina. There are three combinations, all which arrive in Buenos Aires within three hours of each other and all connections of which are on the same airline: LAN via Lima, arriving 7.05pm, Aeromexico via Mexico City, arriving 8.50pm, and AA via Miami, arriving 9.50pm. Of course, this jives with a possible Salta sighting.
Unlikely: Brazil, Chile, Bolivia, Venezuela, Ecuador, Peru, the Guyanas
Possible: Colombia, Paraguay, Uruguay
Looking good: Argentina