Chances are you are not going to get full value unless you can prove total destruction. The burden of proof will be yours. Typically the carrier would offer less than half for the amount. You will have to have some legitimate document showing replacement cost. You would probably show the cost of having a new set made and the issue would be depreciated value. I would continue to insure for full value as you are doing because the cost is so little. Biggest problem? You are a small fish and USPS, UPS, FedEx have more lawyers than the Justice Department. However, under $1000 will usually get paid in a year with some legitimate docs. It is a pain!
Jim