I lived in Melbourne for a number of years but at this stage I haven’t mapped it. BUT I have a really popular trail in google maps designed by David Blom from his extensive knowledge of Melbourne tracks. This 640km bike trail has no overlaps and no there-and-backs. I knew Melbourne had good trails but a continuous trail that long, not possible. I have done a bit of verification, yes it is all bike trail and it is not on any major road at all. Here it is, a full bike pilgrimage in a major city in Australia. Click here to view in Google Maps, this trail is really good.
So in summary, Melbourne has lots of trails and none bigger than this.
600km loop trip. But in reality, look for the stations (I have marked some on the map) as you will need to return to the start. Melbourne trains are fine with bikes.
Don’t read your map on the phone while riding.