Begin checking from the middle of the current month for redemption availability for 6 weeks after. Your best bet would be in the last week of say July for early September.
You'll also need to be extra flexible, does it have to be MUC? why not FRA, HAM, DUS, GVA or ZRH? Look for seats into SYD/MEL/ADL/AKL too.
Lastly, F fares out of Italy aren't that steep so might worth looking at those.