Is there a specific reason you don’t want to use the gift card to pay directly? We leave a credit card on file just in case. But I just pay for most things with the gift cards. If you want a list of what you spent on it, you just have to enter it into the Disney Gift Card site. You can see a list of all transactions on that card.
If you do set up & use charge to the room, you may end up with several holds on your credit card. Every time you hit $100 charged to the room, they place another hold on your card. They do eventually fall off, but just something to be aware of.