Get a loan to pay off the credit card - I agree this is the right strategy. Keep trying until you can find one.
Cut up the credit card.
I think you are doing all the right things - I wouldn't try and get a repayment plan until you are certain nobody will give your friend a loan, it's probably still higher interest rate than a loan.
Like MandM, I do despair at how people can be so stupid as to get themselves into this kind of a mess, but I've seen it first hand in my own family so I know it happens to the best of us. good luck. You are a good friend. Just don't lend him/her your own money.