I wish I had the time to compare the timeline here to that of the investigation of the Limbergh kidnapping; my suspicion is that the amateurishness was similar.
PBS American Experience: Lindbergh was made in 1990. It’s not on YouTube, but you might find it somewhere or on the PBS website. They cover the kidnapping pretty well.
Lindbergh paid the ransom, but he used gold notes. When FDR outlawed gold, he also called in the gold notes. The case broke when a gold note (by then unusual) was used and traced back to the guy who picked up the ransom money. He claimed to be innocent of killing Lindbergh’s son, but wood in the rafters of his garage matched the wood used for the ladder.
Still trying to figure out how he had the power to outlaw gold.