Sadly, the moral of the story seems to be that the 1943 FBI had loads of zealous (performative?) plods on staff, but ~zero law enforcement professionals. In '43, the US had plenty of highly competent professional cryptographers, who were quite experienced with current Japanese, German, Italian, British, etc. codes. Before an entire local FBI office spent even a day on this case (let alone 6 weeks), maybe they should have asked some of those professionals to look at the supposed "Japanese code key" page? If it turned out to be a known code that (say) Canada used for low-security consular messages, that'd quickly narrow down or close the case.

EDIT: If they believed the "Japanese code key" page might be genuine, why didn't they pass it up to the professional code-breakers ASAP? Sitting on it, while the Japanese used the code to plan an attack on the US, could make that local FBI office look like a bunch of idiots and traitors. So perhaps they did pass it up, were told that it was a waste of time...but didn't want to accept that answer.