Here's a radical idea. I know you want to return the land to native species, but as step in that process, how about introducing other non-native plants (already rampant in Australia of course) that would choke out the grass? Is there any such plant? I'm assuming it would be a vine of sorts.

Another option is a plow, a complete eradication of everything, roots and all, then an introduction of a ground cover plant that would prohibit grass, then planting trees in that.

Bamboo? Have you considered bamboo?