Had you booked this with a reputable agent, they could have gotten the cruise line to charge their credit card for half the cost and refunded the difference back to your card. We do this all the time for our clients.
If your broker refuses to work with you, then you really don't have any option except to request a check from the other passenger made payable to you so you can pay it towards your credit card bill. (They could also send the money to you via PayPal if both of you have an account. If not, it's real easy to set one up - we do this alot, too.)
Sorry, just no other way to get that done if the broker is unwilling to assist you.