The three categories make a world of difference.
Under these headings I'd be for starting all over. Many of the suggested songs will not fit under these headings.
So these songs do not need to be well known then? And they need to have been written here?
OK for starters:
1. From Don Henderson -- "The Plastic Song". Early comment about an environmental problem. Rowan's mentioned the other one that come's to mind.
2. The 19th century miners' songs -- possibly all of them except "I'm Going Back to Bendigo" which is about how it's fun to be a miner.
3. All the convict songs that were written here. (a note of caution -- many of them weren't)

Cheers, Joy