The Carstenz Pyramid is interesting, but holy cow is it expensive. Also, getting a great view from the summit always seems to be an issue. It's rare to see a summit picture where it's not smothered in mist and clouds.
I've climbed Kos, not by driving up, but by packing in from Victoria in a week-long trip, hut-to-hut. So I'm sorry to see that my sole 7 Summit claim is laid waste.
However, the highest point actually owned by Australia (the Continent) outside of Antarctica is actually Mawson Peak (9,006 ft), on Heard Island. I'm nominating it as the Australasian highest point. Not only is it a difficult trailhead to access, the bloody thing seems to be in the process of blowing up!
Now, that's a challenge.