So with bags to check in it seems your options are limited. If you have to arrive at the airport that early, then Baggage Storage seems your best bet. It currently costs
AUD8 per piece for up to 6 hours.
In the case I mentioned above, I had flown up from Melbourne that morning arriving in SYD at 10am for a 6pm flight. The agent made a 'phone call and had the flight "opened" to enable check in; immediately my BP was printed the flight was diligently "closed".