Thinking outside the square, I looked availability for the OP on EF on the mentioned dates ex-MEL, SYD, ADL, BNE, and PER with +/-3 days margin. I even looked ex-AKL.

The only available combination was PER-DXB-TUN on 28-Nov, return on 30-Dec. Each with almost 12 hour stop in DXB and an awkward arrival time to PER on the way back. The upshot is the lower cost in miles for upgrading.

EK423/EK747 and EK748/EK424. But the OP needs to be quick, there's only 1 seat on the PER sectors. He can book a MEL-PER-DXB-TUN return on EK, then call to upgrade the EK sectors. Unfortunately he won't avail the chauffeur drive in MEL, nor be able to fly MEL-PER in J.

Hope this helps.