A further update, flew with 2 cats (one in-cabin and one hold) LAX-SGN via ICN with Asiana in May 2017. Extra cost was USD$200 per pet. Required rabies vacc and health cert from USA. No dramas on arrival in SGN and we exited baggage claim with no hassles.
My BIG concern though, they changed equipment and flew us on an A321 (instead of an A330) from ICN-SGN with no notification of the change. Asiana's policy is no live animals on their A320 series aicraft as these are not suitable for live animal carriage. My issue is the risk my animal was exposed to flying on an unsuitable aircraft and after repeated emails, calls and Facebook messages I have yet to receive a proper response from Asiana. Very disappointed.