I did call Amex and they referred me to their insurance team, who offered to cover me for around £250 pa. No extensions offered even with a surcharge - but I guess I expected that.

What I did not expect is their inflexible 'tough luck, you just have to accept it' attitude. I suppose loyalty counts for very little these days. I have been an Amex cardholder for most of my life and a platinum one for 20 years.