I have done 2-3 AONE3s each year for the last 4 years, and I have never failed to get on a flight I wanted to get on except when delays caused missed connections, but even then I have been able to get the optimal reroute without difficulty. Maybe I just pick strange times/places, but all the recent ones have included HKG-JFK.

Occasionally I have had to invoke status (Diamond) but not often.