Other options include starting your award journey in SYD/MEL and then booking a cheap flight with cash (if one is available) from AKL to the starting point of your journey. Or... booking with AsiaMiles from AKL to a point in Europe like LHR, HEL, etc and then booking a cheap flight from that gateway to FCO.

Is this 100% "free" the way an AKL-FCO redemption would be? No. But depending on how much the connecting flight costs, it can still represent an enormous savings compared to the cost of buying a cash ticket AKL-FCO.

ETA: There's mid-week availability on AKL-HKG-LHR in either economy (70,000 miles) or premium economy (84,000 miles) in either of the next few weeks, so far as I can see. You'd then buy a ticket LHR-FCO (on BA running around GBP150). That GBP150 cash outlay is guaranteed to be markedly cheaper than buying an AKL-FCO one-way flight without using miles on the long legs of the trip.