DOT has dinged a few carriers for routinely taking 8+ weeks.

The chargeback route, presuming that you have used a US-issued CC (or another country with similar chargeback rules) is far the best way to go. Just request the refund from the vendor, e.g. CX, give it 7 business days and on the 8th day file the chargeback dispute.

Advantages are that you receive an immediate temporary credit which restores your CL if you are concerned about that, forestalls interest accumulation, and puts the shoe on CX's foot. Given that CX has already agreed to the refund, it won't do anything and, in due course, the temporary credit will become final.

On the other hand, if the CX refund arrives in the meantime, the card-issuer will match it up with the dispute and the temporary credit will become final sooner.

Bottom line here is that time is money and it ought not require multiple calls to get anything done.