I have made a similar claim (luggage damaged not delayed) through my HSBC premier insurance a couple of years ago.

Airline only agreed to pay up to a certain amount to replace the luggage (could not be repaired) as they were devaluating my luggage due to years since bought, however I put a claim for the difference via the insurance and received the top up payment (minus the £50 excess). I believe both HSBC Premier And Amex Travel insurance are actually offered by AXA but terms may be different