I have a credit card that is at 22.24% interest rate. I have been paying an extra $25 every week and a larger than minimum payment every month. I really would like to transfer the balance, but I hate paying the large fees that sometimes come from that. So I got an idea...What is I charge a large purchase that I would normally pay for out of my checking account to the card with the lower balance (ex my $220 a week grocery bill) and then take the $200 from my checking and pay it to the high interest credit card. May take a couple of weeks, but eventually the card with the lower rate would have a higher balance and the card with the higher rate would have a lower balance. My checking account balance remains the same -- and no balance transfer fees!!
The plan you have outlined should work fine provided you are organized and use restraint (do not spend more than you have been spending on groceries etc). The potential problem with this strategy is that you are basically moving everyday expenses you pay for with cash to a credit card. I understand why you want to do this and it will work, but if you get off track it can lead to racking up large cc bills.
Good luck--your credit card debt will soon be history.
Make up a spreadsheet with your balances and charges. Update it with each transaction. That way you will be sure you are working toward your goal.
Many people say "stop charging and pay with cash". That isn't necessary if you actually keep track of where you are financially. It is easier to charge it but if you keep track, you can be better off charging almost all your expenses.
Edited to add: Don't ever charge something that has an extra fee to use a CC such as property tax.