Different countries (and often different consulates of the same country) follow different rules, and sometimes those rules can be bent.

I'd call the Paraguayan consulate closest to you now (LA?) and explain the situation. Ask whether they'll expedite it from LA, or failing that whether you can get the visa in Athens.

When I went to Paraguay (admittedly it was almost a decade ago), I remember that the NY consulate processed my visa within 24 hours.

For what it's worth, when I was in Paraguay on that trip, I was able to get a Brazilian visa issued next-day at the consulate in Asunción. Didn't have to do that in my home country.