https://flights.app.goo.gl/S6kBR
Seems to be May 24 - EOS.
Availability is wide open. I am finding the DFW-ICN-SIN flight with an hour layover, but also some Delta One Suite options through Detroit and Narita.
Books into Z class with a $450 change fee and is non-refundable. Stopovers permitted at $100 each.
Momondo shows plenty of routing options on Korean through ATL, JFK depending on which Korean plane you want, 777 or A380.
Alaska Air seems to be the best credit partner, especially with tier bonuses.