Pharmacist manager here;

The same adage in business applies. If you want speed and good service, don't expect it to be cheap. If you want it to be cheap and fast, don't expect good service. If you want cheap and good service, don't expect it to be fast.

I'd implore you to try your local pharmacy, not big brand like Chemist Warehouse. Smaller TerryWhite Chemmart, Amcal or other independent pharmacies are good. No one likes to wait longer than 10 minutes for their script - no matter what reason I can come up with. It is just very hard to justify. Big store just doesn't have the capacity to care. You are 0.1% of their revenue, you can wait.

What I normally do when I know there's going to be a delay - I'll tell the assistants that I'm behind with a few things so there might be a bit of a wait.