It's a CASA issued ASIC (as opposed to an airport issued one)? Maybe you can lean on them a bit??
When I ordered my ASIC - they sent me someone elses! It turned out that the "someone else" had received mine. The fellow at CASA kindly asked me to express post it to that fellow, as he needed it for work within a couple of days.
....I'm not sure if they can speed up the process, but it seems that they do understand that people need these to earn a living.
I have also heard that there is a small company out there somewhere (maybe there are several) that handle the ASIC application process for you (can speed things up?). Unfortunately I have no details on hand. If you can find it, they might be able to help in this situation.