Claim claim claim, tell them their exclusions are rubbish, if they accept it for shipment it is their responsibility to take proper care of it.
Easyjet damaged my guitar case, luckily they managed to do it without damaging my D28. I notified the ground staff of the damage, and they took note of it, and I filled in the form they gave me and sent it off. In the meantime I needed to fly again with the instrument so I invested in a Calton case which cost twice the price of a Martin case, I sent them the bill expecting them to leave me to pay the excess for the dearer case, and to my amazement they sent me a cheque for the full amount.
Moral of the story Easyjet are not as black as they're painted, and push push push for compensation for your damaged goods.
Good luck with it.
Giok