My response would be "I chose to shop at this business based on the payment methods you chose to advertise before entering into the transaction, which included American Express. I remain willing to pay for my bill using American Express, being a payment method you advocated as available for this purchase before this transaction was entered into. The fact that you are not in a position to accept that payment is not my responsibility - and the fact that you've gained my business (and likely the business of many others) by making false and misleading claims is a matter that I can refer to the ACCC. Again, I am more than happy to settle my bill using AMEX, a payment method you advertise as accepting. If you cannot process this payment, I'm happy to pay you by PayPal or RewardPay - which can be funded by AMEX - but you'll be covering the processing fee."
(The 'transaction' being an exchange of goods services for money at the advertised price.)
Have taken a similar approach at restaurants that get you through the door by having a large "AMEX CARDS WELCOME" sign on the front door, make no mention of an AMEX surcharge on the menu and then attempt to add one when you pay - although that discussion is much briefer as a simple "you did not lawfully disclosed the surcharge before the transaction was entered into, so you cannot legally require that I pay it, and I won't be".