If your primary interest is getting past security and into a lounge for sleeping/showering (and you are not checking any baggage), consider buying a fully refundable business/first class fare on the airline of your choice for a flight that departs at a time that allows you to check in for it upon your arrival in SYD (or just before your departure from PER).

After you've rested, cancel the flight, exit past security, and go check in for your AC flight.

Presumably, you would want your refundable ticket to be a domestic one, so as to avoid immigration and customs matters.