From the initital description, this sounds like it could be a married segments rule/behaviour coming into play.
[An airline could take a view that it can still sell tickets X to Y for money, so will not make any more award seats available. But, it might not be able to sell many tickets X to Z via Y, so will make that available for awards. Hence you can get the behaviour described quite correctly.]

But before writing it off, do you have any other access to check oneworld award inventory?

You could signup to AwardNexus, and try the Qantas (QF) award search. [Will leave you to do that one yourself, rather than use my own credits. You get 100 free, and can refill every 90 days.]

Assuming it is economy you are looking for, ExperFlyer can also see that for finnair.
And it is showing 4 economy award seats available on the flight, regardless of whether you search YYZ-HEL, or YYZ-BER.