The issue here is what if the chargeback as promised never materializes? By then the chargeback window has expired so what other window of recourse do you have to get your money back if the airline fails to follow through?
Can the credit card company keep the chargeback open until you get the refund? I would try any means possible to not allow them to close/deny the chargeback until you have the credit...
Also a good card issuer would issue you a provisional/temporary credit and then reverse it once the official chargeback goes through. Another thing you could try to ask for.