I have a non-marriott AMEX card on my Marriott profile...

Back in June I checked in at the Sydney Circular Quay Marriott and gave the front desk a Marriott Visa and asked that charges be put on that card. When my automatic bill was slipped under the door, there was no CC information on it, so I assumed that the Marriott Visa was used - however the AMEX was charged. I assumed that it was my mistake after a 23 hour flight...

I had a similar experience this month, where I explicitly gave them the Marriott Visa at check-in and told the front desk that last time my AMEX on the profile was charged and that I wanted the Marriott Visa charged. On the day of check-out, the automatic bill was slipped under the door, again with no CC information. This time I walked down to the front desk to verify that the Marriott Visa is being charged. The front desk indicated that there was only the AMEX on file... expressed my displeasure and handed over and asked again that my Visa be charged as this is the second time it has happened.

I asked the front desk if I could switch the charges of my previous stay to the Marriott Visa, and she spent five minutes on the computer to finally print out the previous bill indicating that I paid with an AMEX and said "show that to Marriott Rewards". Sensing that she did not understand my request and not wanting to be late for my flight, I left.

My question: How can I get the first stay switched from AMEX to a Marriott Visa?