To repeat my earlier comment, remember that these confederate inspections were done in Britain, and so don't prove the inspected arm actually reached the south - lots of cargoes bound for southern states were captured, sold at admiralty prize auction in New York, and were bought by New England states to arm their Yankee troops:
Your enfield would have been inspected by a "viewer" in Britain who was inspecting as part of a confederate purchase, but as you say, plenty of arms were captured and sold at Northern maritime auctions to the highest bidder - so those arms didn't make it to southern armies. One famous example is that the state of Massachusetts bought a load of captured arms inspected for the South for their troops, and stamped the brass of those arms for several Massachusetts regiments, and so those arms have "official" stamps for the South (viewers marks showing confederate "viewers" accepted them as to quality in Britain) and for the North (the state property marks put on by Massachusetts after that commonwealth bought these at admiralty "Prize Court" sales after the ship carrying them was captured).
Also, arms inspected had to be paid for before they were shipped, and if the confederate buyer didn't have the cash or credit when time came to conclude the deal, those arms might have been snapped up by a union buyer, and so never even loaded onto a ship bound for the South.
I would not be surprised if Connecticut bought some for its men, including perhaps your ancestor's unit.