Trying to use SkyMiles for 2 economy tix one way MNL-JFK. delta.dumb shows availability for a well-timed MNL-ICN-JFK itinerary. Website does the 'flight sold out' message at the last part of booking. Called into the call center to book, they saw the flights and started to ticket, then said the ICN-JFK leg wasn't actually available. Hung up. Went to expertflyer which indicated no availability on those flights. Set alert. Got alert 6 hours later showing availability. Logged into expertflyer, still showing availability. Delta.dumb also showing flight bookable (but same flight sold out message at end of ticketing workflow). Call into call center, get call back 2 hours later. Agent sees availability, starts to ticket, puts me on hold, comes back with ICN-JFK leg not actually available.

Haven't dealt with a booking like this in years, or a KE booking ever. Is phantom availability thing here? Any way to figure out definitive availability or secret words to ask the call center reps to get this thing to actually ticket?