Is it too late to check Martin’s fingerprints against those found at the burglary locations? If there are any found.
How about checking whether the women's jewelry that was found in his possession had any serialized diamonds, and checking whether any of those serial numbers were reported stolen? Many diamonds are engraved with serial numbers, and many jewelry stores record those numbers on the purchase paperwork. This protects the store and the customer from fraud, and also helps protect the customer from theft. I don't know how much women's jewelry TM had, or what quality it was, but it would seem like honest cops should want to check whether it was stolen.