Some additional info, this from Sharps Firearms - Volume 1. The Percussion Era, by Roy Marcot, Ron Paxton, and Edward W. Marron. This is a great book, volume 1 of 4, hardcover, 495 pages, with plenty of excellent color photographs of just fantastic examples and accessories from various collections. It's very well researched and thorough, and you can still buy autographed copies direct from the author. Volume 2 covers the Sharps guns of the metallic cartridge era and is equally as valuable on one's shelf, IMO.
It has this to say about the New Model 1859 Sharps Carbine:
"One of the true mystery carbines of the Civil War was the New Model 1859 Sharps carbine known as the "Navy Model." The wartime facts around the carbine remain vague. From the start of the war to the end of September 1862, the Federal Army commanded the inland rivers, including the Mississippi River. The Army Ordnance Department purchased and armed the naval vessels with Army crews led by Federal Navy officers. In the spring of 1861, William Nelson was sent by President Lincoln into Kentucky to organize and recruit for the Union cause. In July, from Cincinnati, Nelson wrote to the War Department requesting 300 Sharps carbines for the Mississippi Squadron in the process of being formed by the Federal Army.
Nelson's request for 300 Sharps carbines was sent by the Ordnance Department to the Sharps Rifle Mfg. Company. At this time, the Sharps factory was in the process of finishing the Navy's "Mitchell order" for 1,500 Sharps New Model Military Rifles. The Mitchell contract rifle serial numbers are found up into the 42000 range. The serial numbers of the New Model 1859 Sharps Model Carbines are in the 43000 range. Since the carbines were for the Federal Navy they had no use for a sling bar on the receiver, it is possible that the factory took the leftover parts from the Mitchell contract to fabricate the carbines.
The New Model 1859 Sharps Navy Carbines had a rifle receiver and rifle buttstock with sling swivel, and a standard carbine barrel. The 300 carbines were sent by the factory to the New York Agency, where they were inspected by the Army inspectors. An inspector's cartouche was stamped on the left wrist of the buttstock. Army records indicate that 300 Sharps carbines were purchased for the Navy on September 3, 1861 at a cost of #30 each.
The author goes on to say..
"The Navy Bureau of Ordnance records and Deck Logs from the National Archives do not show these carbines being issued to the Mississippi Squadron. Ships logs of this squadron during the Civil War do not show receipt of New Model 1859 Sharps carbines, although several vessels were armed with Sharps New Model 1859 Military Rifles. The 1866 official Navy inventory listed only a few Sharps Model 1855 carbines. It appears that the Sharps New Model 1859 carbines may have remained at the New York Agency storage facility throughout the war. The carbines would not have been issued to Federal Cavalry troops because of lack of a sling ring.
The Sharps New Model 1859 Navy Carbines found in today's collections are typically in very good or better condition, confirming the view that they were not issued."
There are additional details about this gun's unique characteristics, and the sling that was used with these, including some great photographs of them. The sling was basically looped around the barrel via a simple buckle, and then back through the sling swivel on the stock.
This book has new (to me) information about the order for the carbines and speculation on how they were put together. Notably, he finds a request (order) for 300 carbines and ties them specifically to the Mississippi Squadron being formed by the Army.
While theories on the employment of these guns is limited to dueling speculations, it's notable that Marcot's recent book conflicts a bit with McAulay's earlier research.
Rereading what McAulay wrote in "Civil War Sharps Carbines & Rifles", as quoted earlier, the letter from the Secretary of the Navy isn't indicated to have itemized
these carbines specifically, so much as the disposition of "guns" coming off the boats generally, and so it seems a speculative link to assume the carbines were included. To revisit McAulay's question, "how did these end up in the hands of the army", may be answered by Marcot's theory - bought direct by the Army, placed in New York at storage facility and never deployed.
McAulay had also speculated in another book, "Civil War Carbines, Vol 2", that these guns may have been purchased by a Navy agent through a private dealer in Philadelphia, Joseph C. Grubb and Company. The additional research represented in the 2019 book by Marcot, et al, pays out here too - there's an actual order from the Ordnance Dept. direct to the factory for the 300 carbines. That seems to solve the acquisition mystery.
So were they ever deployed? Maybe they stayed in NY until sent back to Sharps for conversion, then shipped out to Ft. Union because they didn't know what else to do with them. Probably not suitable for maritime work. Definitely not suitable for cavalry work. Just a misfit, el patito feo. As it was said, these are "one of the true mystery carbines of the Civil War". A rare piece, a custom variant requested for a unique application in the war, that much is certain.
I am ever in awe at how much hard work and research is on display by my elders in the gun collecting world. Digging through National Archives, looking for the most obscure source material, pouring over factory records, to say nothing of the travel required to make all that possible, then compiling these books. In the age of Google, so much knowledge is still offline.