I searched SYD-CPH last week and found nothing, but when I entered SYD-HKG-DXB-CPH - it offered me seats. You just need to know the flights you are targeting, so that you put the right date in so Day 1 - SYD-HKG, Day 2 HKG-DXB (is only a 2.5 hr connection even though next date) and the Day 3 DXB-CPH.
The search engine behind the classic reward search often isn't that smart and doesn't always show all availability, as its default routing may not be the only routing.
Also I could find nothing in J all the way home, but when i mentioned this to the girl on the call and that I was flex in routing as long as no more than 3 flights and I was home by the Sunday, she asked me to hold while checked and then found HEL-DOH-SIN (on QR) and SiN-SYD (on BA) which were never shown to me using the tool even though I looked at that combo.
So if you think there really should eb availability, invest the time to call, as soon as you say it isn't showing online they waive the assistance fee anyway.
