I give the front desk my Disney CC card, then charge everything to our KTTW card. Every evening or every other evening, I get a print out - we don't find it hard to keep up with purchases for 24 or 48 hours, more or less and we know at the end of the day(s). Right before we leave, I go online and transfer money to my Chase Disney rewards card to cover our bill. Anything extra goes on the CC, along with all our Universal Parks charges (we've gotta go to Hogsmeade at least once!) and our charges going and coming), then I pay it off out of our vacation savings account as soon as I'm sure everything is on the card.
I'd rather pay with a CC when I have to use cash money (i.e. not reward dollars) because it has the most protections for travel - you can dispute charges, you have rental car insurance etc. - and I get points for my next trip.