That's pretty awful advice, even if it's often voiced on FT. There is no grounds for a chargeback. When CX first charged OP's card, it was with OP's permission in exchange for a service OP intended to use. From that moment on, this becomes a matter between OP and CX. The bank isn't interested in getting involved because a.) the bank has no insight into original terms of OP's contract with CX, including any terms governing refunds, and b.) the bank has better things to do than mediating what is essentially a commercial dispute between OP and CX over whether CX is honoring that agreement by refunding in a timely way.

In the best case, initiating a chargeback is a waste of time. In the worst case, making a habit of it can get people branded as problem customers. It's best to save the chargeback for what it's intended for: Fraudulent use of the card, or instances where the merchant entirely fails to deliver a service and the customer really has no other recourse. Here it just took another call or two to CX.

Afraid you're also going to be out of luck on this one. I haven't looked, but I'd be surprised if they did not include a clause somewhere in the conditions of carriage or some other legalese that absolves them of responsibility for consequential damages such as this. Makes sense -- they can't be held responsible if a particular customer's credit card balance results in a higher interest rate in this kind of situation.

Although it might not be much comfort, I'd look at it this way: Over the years you've been flying (whether on CX or other carriers), you have probably saved an amount by buying restricted discounted tickets that you flew as planned that is far greater than the amount you've lost in this one unfortunate incident where things went awry.