Had you ever had the ring appraised, perhaps for your insurance? If so, that might enable you to claim more than the original purchase price -- assuming that the ring was appraised for more. And an appraisal might be an acceptable substitute for the original sales receipt.

Edited to add: Unlike many other chattels, a piece of jewelry can appreciate in value over time. If it had been appraised nine or ten years after purchase, its value then might have been much higher than the purchase price.