On my calculations your course from Cairns to North Cape direct on the great circle is initially 130 becoming 118.
Cairns is at 17 s below the E winds and the trades will be SE down to around 23-25.S more or less Brisbane.
I doubt that that boat will go closer than 45 to the true wind
. So you have a choice between 67 and 157.
The south current will mean that you actually make good roughly 90 or 170.
That suggests to me that you will need to head east for a while on stb unless you get a more favourable wind
to clear the coast then take the port tack which won't put you far away from Brisbane. There you start to pick up W and SW winds.
If instead you just continued on stb tack you remain in the trades probably with the current becoming against you not assisting you.
Just my rough thoughts. Dana-tenacity has far more experience.
As an aside I see you mention "saw the boat". I hope you have had enough time already to do some shakedown trips and check all the gear