Has anybody tried getting Australia's departure tax refunded for being a transit passenger on two tickets?

I have two tickets. The Passenger Movement Charge has been included in both tickets. One is SFO-SYD-SFO. The other is SYD-AKL-SYD.

I'll be travelling SFO-SYD, SYD-AKL, AKL-SYD, SYD-SFO. On my return from AKL, I'll be in SYD for four hours before my SYD-SFO flight departs. I believe I'll be entitled to a refund for one of the Passenger Movement Charge as a transit passenger.

Since the charge has already been included on both of my tickets, how do I obtain the refund? Thanks.