Have you tried to price your itinerary directly to EZE with Varig ? You should get a free stopover in Brazil. If they don't let you stopover in RIO and make you stopover in GRU then a SAO-RIO (rt) is available starting at USD 50,00 flying an LCC.
Editted to add :
Notice this is the OW forum !!!
Try the above with TAM airlines - probably an AA codeshare might be more expensive. Beware that by flying TAM you may accrue miles in AAdvantage but if not AA# they won't be EQM.