Probably the best idea, try to resolve it at the source. If that doesn't work then Amex should be the next step.
Question though, here in North America we have what's called the Better Business Bureau (BBB). They are a non-partisan organization that acts as a third-party to resolve consumer complaints with businesses or charities. Is there such an equivalent in Australia? Forgive me of my ignorance. I've used them on a couple of previous occasions with great results, and I often find even threatening to file a claim with them will generate the results you want out of a business. Having a complaint filed is like a big red 'X' on their record for all to see so they try to resolve issues in-house when they think the customer will press on.