Hi Jove,
Trust you mastered the "every other day" and got on the refurb one, yet time in the Eternal city would have been great.
The lounge next to First has the most showers, latch onto an attendant and she will give you the towels and slippers.
You will have time so don't worry.
I have not been able to plot any specific gates for Melbourne, except that it is always the last possible one

If a holiday, hope it was memorable.
FYI, SQ offering BKK-MEL -BKK for 1000 incl, not a bad fare
regards bkkrop