It may be no comfort but we have a difficult time getting insurance claims accepted here at work. We ship a lot of our products (we make point of purchase displays) through UPS and don't screw around with packaging. Our displays are packed in custom sized cardboard boxes, braced with cardboard fillers and cushioned with blow foam. We also "Drop Test" everything which entails packing a display for shipping and pitching it off the loading dock. If it survives its a good pack out. For some pieces we even ship it cross country and back to test it.
Yet, still, when a display arrives broken, its a wrestling match. We usually win but it takes a while and we do mucho $$ worth of shipping with UPS.
Wish I had an answer for you. Next time you might want to have the UPS store pack it for you so that you can go after them if it arrives broken.
T