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I know you mentioned you hadn't had any luck with recruitment agencies, but have you only tried general service providers, or those who specifically cater to those in the legal field (ie. Law Staff Australia)?
For a comprehensive list of job sites and online portals that you can use to look around, you can also have a look at the Expat Arrivals Finding a Job in Sydney page.
Otherwise, as painstaking as it may seem, I would recommend using LinkedIn groups and Newcomer's Associations to at least plant the seed that you're on the market.
In the end, it's crucial that you keep chipping away.