Thanks for the resident interpretation of "cop some stick." As usual, the explanation only raises new questions. I believe it was Barbara Horvath (long-term Sydney resident), the wife of my former graduate advisor, who coordinated the linguistic studies that you refer to. Maybe I'll send her an e-mail and see what she can say about the phrase's evolution and dispersion.
It does sound like you're in a major heat wave, with bush fires encroaching on Sydney's northern suburbs in our worldwide news reports. Hopefully the beer is still cool!