Not sure if this is any help, but just wanted to say that I hope you are also getting some assistance from the hospital with the emotional side of things. There should be an oncology psychologist or counsellor I would think, and if that person doesn't seem right for you, your GP should be able to send you to someone.
If you feel you'd like a second opinion, RPA is I believe the biggest liver unit in Sydney. Some of the surgeons there are involved in research collaborations with people from the US and Europe. When we were in Sydney 3 years ago the oncologists also had clinical trials going.
Regarding genetic testing, we had it done last year, had to pay the full amount though as it is not covered by Medicare or private insurance. There is an office for one company in Sydney and they send the samples to the US (results were back in less than 2 weeks). I believe the Garvin institute will be sequencing patients samples at some time, but they were not ready last year.
Good luck with the testing results.