Guest: Thanks, I tend to agree with your conclusion, but we're trying to "Nail it down" conclusively.
I've been in touch with Kenneth Wooster, who keeps a website for "The 12th New York", but who was unaware of the song. I feel the salient point of his reply is worth quoting in full (for now)

"Nevertheless, I think that the song sheet can be dated to some time between April 1861 and February 1862. The 12th Militia existed for many years prior to the American Civil War as a unit of the state's civil guard. They were sent into Federal service for three months at the outbreak of hostilities. From here the history is confused and confusing. As you will notice in the first few paragraphs of my file at 12th New York that the organization continued to exist more or less as the 12th NY State Militia (sent into federal service) until in February 1862 it was consolidated into the newly formed 12th New York Volunteer Infantry Regiment. Although the 12th Militia was reconstituted after the war, I believe that it did not exist as an organization during the American Civil War after February 1862. Thus my end date of February 1862, and since the lyrics speak of the southron [sic] rebels the words must have been written after Fort Sumter was attacked in April 1861. "

This gives us a very short period for the origin of the "12th New York" version.

Nigel