Sorry to hear about your phone. If there is one thing I have learned is how valuable AppleCare is. It has saved me, so I insist on it for every Apple device I buy.
They might replace it for you anyway but it's highly unlikely. Just fork up the 150 for the new screen and next time just get square trade or apple care +
Problem is, nearest Apple Store is almost 2 hours from here. So takes a bit of planning. Maybe I'll try and take it there and see what they say. Thanks!