AV: JFK - LIM, $660ish
Avianca, JFK - LIM with a stop in BOG/UIO, several dates in April 2018 (April 11 - April 22, +/- 3 days), $660 or so depending on booking site.
Also can add a stopover in UIO for a total of about $730
Most flights are on A330 which should be "angled flat", I think. Or did Avianca complete the switch to the new lie flat seats?