I did a KE F award from LAX to ICN off peak and there was plenty of availability.
Only 2 of 12 seats were taken on that A380 flight.
Some dates for Biz award were not available though.
Read that OZ is also going to use a A380 from LAX to ICN but I don't know when.
U might also want to consider the cost of award tickets.
It's about $300 or so for KE.
Don't know about OZ via UA.