AFAIK DL's only South American service at this point is the ATL-GRU flight, although there was a good deal D1 fare to Chile reported earlier this month showing a scheduled flight from ATL for November IIRC.

I'm not sure whether it would wise to book connections into EZE using some of DL's local partners at the moment as they seem to be having financial difficulties.

OTOH, fully refundable hotel reservations could be a smart move if you see especially good rates. Just don't forget to cancel them if the situation goes south so that you can't go south.