Have you tried calling them? Things may have changed, but several years ago I contacted them about parts for a suitcase, and they were very helpful, and responsive.
You could also try googling "luggage repair" or some such to locate third parties that might be able to supply the parts.
Between the camera cases, equipment cases, and luggage that Haliburton has made, there are lots of their products around. Certainly partially broken ones exist, I've seen many in flea markets and shops selling tech salvage stuff. Ebay might be a workable source.
One other possiblity might be to see if you can find out where Airlines send the cases they've done settlements on. Though getting to the person who could tell you would probably be very difficult.
I traded a smashed Haliburton to Delta for check once but I have no idea where the case ended up, it's probably a Pepsi can now.