I think their room charging policy is great! We have gone and left our Visa check card at check in and they have given us credit limits above what we had in our account! It is too funny. Anyway, we were at a moderate so we had the $1500 limit, but we only had $900 in our account. We left them the credit card, (they don't put any type of a hold on your card which is great, because if you want to use it at a shop instead of charging to the room you can) and then the afternoon before you check out, you just go to the desk and tell them you want to pay off your balance, or like you said, go pay with cash or TC every couple of days to ensure they don't charge you for reaching your limit. They will only charge your card if you hit the max for the resort, or the night before/early morning of your check out date.
Many times I have also sent money in every few weeks to either pay off the room, or have added to our account for spending. We have never gotten any money back-but that is our fault not Disney's-we spent it all!