OZ is a toughie. I tried to get a a work visa through sponsorship while I was there and was told even if someone wanted to sponsor me, I would have to leave and come back when it cleared. A visa run if you will.
A friend of mine married an Aussie but they met here in NYC. She was able to live there a few months at a time but she had to keep doing visa runs (NZ, Fiji, etc) until the married papers processed. A hassle but better then going all the way back to the US.