I had very limited exposure to the classification system for government documents during my time in ASCS/FSA. IIRC ASCS did get some classified documents as part of the distribution system for the agricultural attaches stationed in some embassies. I'm not sure why some, a few I think, were classified; perhaps the attaches had a report on the status of a nation's crops which were obtained by befriending a statistician--I don't know. Anyhow, a management analyst in Records Management had a clearance and handled them. I suspect the whole setup was a carryover from New Deal days, before USDA silos were built up, possibly before Foreign Agricultural Service was formed.
Anyhow, I'm not surprised by problems in handling and tracking classified documents. You might be able to have secure handling if you used a dedicated database with no ability to copy, download, or print. That way you could track the user ids anytime a document was read. But, with the possible exception of the most highly classified, that's not practical. (It does seem that when documents are viewed in a SCIF that while they could be printed, nothing could be taken out of the facility.
For the more ordinary classified documents, I wonder if they have a system of bar coding or CR coding for them. The problem of course would still be the copying, printing, downloading--how do you assign a unique identifier to the copy, printout, or downloaded document? If election officials and USPS can assign a unique code to a ballot so it can be tracked, but they don't deal with duplication.