I'm not sure a strike from the airline own personnel is classified as Extraordinary circumstances.
I would surely NOT cancel the whole ticket. That would leave AZ off the hook; if paying in advance is not an issue, you can book your own hotel, pay for that and the meals and then ask AZ for reimbursement under duty of care.
Also, do not use AMEX insurance just as a backup: if it's covered, claim for it.

Two year ago AZ cancelled my FCO-SUF return flight due to a strike from ground personnel, not related to the airline. The rebooking option was absurd and there was no way to contact them. I kept the ticket as it was, took the train instead of the cancelled flight and then claimed for the cost. Since I got no reply in 3 months I used a free airline claim service, and 1 month or two later AZ reimbursed the cancelled flight. I then claimed the difference with the train ticket using Amex insurance.