I actually was able to switch after a stay in a non-US property recently. It was a personal stay on a prepaid rate. The computer autopopulated the credit card. It wasn't until after my stay that I realized it was the card I use for online purchases, not my Marriott card, and the hotel was able to swap cards.

Again, that's info under the "can do it" heading. If it's against corporate policy, the OP shouldn't do it.