I would do nothing now. There is no benefit to you to cancel until BA cancels or reschedules or the day of the flight (cancellations & delays occur for all of the same reasons as in the past as well). Should that happen, you are due a refund. You only confront the credit issue if the flights go. In that case, it is down to whether you plan on traveling with BA in the future. If so, the credit is not a bad thing (although sub-optimal when compared to a refund).

While new travel insurance will not likely cover existing tickets, perhaps start looking around. Stand alone policies which cover a great deal more than Amex, are likely available for a great deal less than the Amex fee and if the other benefits of the card are no longer of value, you could achieve savings that way.