My reading on the case suggests that it was badly bungled at all levels. I don't believe Hauptmann was guilty. By the way, if Hauptmann got the money from Fisch then your theory falls to the ground. If Fisch, a con man, somehow got his hands on some of the ransom money and used it to pay a debt to Hauptmann before he skipped the country then there is nothing to connect Hauptmann to the crime. The rest of the evidence that convicted him was faked up or not trustworthy. His attorney handled the case badly, in fact it was the last important case of his career before he was hospitalized with dementia caused by tertiary syphilis.
It doesn't make sense that Hauptmann the master criminal was clever enough to carry out the crime of the century, evade a nation wide manhunt, hide the "hot" ransom money for years, then got caught passing it in his own neighborhood.
His story that he was given the money in payment of a debt and spent it not knowing it was connected to the Lindbergh kidnapping, seems more likely.