USA-MEL is doable on Etihad out of JFK, also consider ANA via Tokyo. Look for anywhere East Coast, or even Perth as you get the connecting flight on Virgin Australia included in the ticket for free. No need to buy additional connecting tickets.
You can also search with a transit in Asia… so ANA to Tokyo, connecting to TG/NH TYO-BKK then TG BKK-SYD/MEL, etc.