I have to agree that Smith's version could very well be a melding of two or more different songs, as you say, Lighter, but given the times and circumstances surrounding their origination it's great that we have the results to analyse, unpick or just enjoy.
Army songs vary from one regiment, barracks and platoon to the next, and sometimes even from soldier to soldier, and because they were rarely written down it was/is considered fair game to amend or adapt them to suit the personal perspective of the singer.
Numerous conscripts and regular soldiers from my own extended family sang military songs, 'MacCafferty' for example, and no two versions matched.
You observation that Smith's text comes second-hand carries the unspoken but valid caveat that much can be missed or altered between the ear and the pen, however unintentionally. Most folkies, yourself included I gather, seem to have an ability to detect additions and verbal weld-ons that don't sit well within the framework of the text.
Cheers, and thanks for the posting.