The description you give of the locking mechanism on the rifle indicates that it has a Mark III action - the carbine has either a Mark I or Mark II action from the sounds of it. In fact, the "Mark" number should be stamped on the top edge of the action "shoe" - i.e. I, II or III, possibly with one or more "stars" (i.e. *) which indicate minor variations of that Mark .... see first image below ....
The Snider system was only adopted as a 'stop-gap' solution for converting existing muzzle-loading Enfield rifles to breechloaders while a 'purpose-built' cartridge rifle was being developed. The original action design actually afforded acceptable safety because the pressure is straight back when the cartridge is fired, simply forcing the breechblock against the rear face of the shoe recess. However, it was discovered that in the event of a cartridge case rupture the excessive gas escape to the rear would sometimes flip the block open .... never with any fatal consequences, or even severe injury, to my knowledge ... but unquestionably very disconcerting to the shooter!
As mentioned in the List of Changes entry for the Mark III rifle (second image below) the significantly improved locking mechanism was introduced at the beginning of 1869, and by that time the existing supply of original Enfield muzzle-loading rifles suitable for conversion had been exhausted (in part because an arsenal fire destroyed a large number) but the Martini-Henry rifle which replaced the Snider-Enfield was still a long way from adoption (that occured in mid-1871). Whereas the Mark I and II versions of the Snider-Enfield had been converted from muzzle-loaders with iron barrels, the Mark III was "built from scratch" using the improved latching breechblock and new barrels made from steel (the barrel on your rifle should be marked "STEEL" on the left side toward the rear .... ) By the way, the "List of Changes in Artillery Matériel, Small Arms and Other Military Stores" was the official record of such things for the British War Department, introduced in 1860 with a name change in 1872 to "List of Changes in War Matériel and of Patterns of Military Stores".)
It is ironic that, although the Pattern 1853 Enfield was one of the finest and most accurate military rifles of its day, the Snider conversions are notorious for inconsistent accuracy. The British War Department went through at least nine distinct variations of Snider cartridge from adoption of the system in 1866 through mid-1871 ... basically they were trying (unsuccessfully) to get the breechloading conversions to shoot with a level of accuracy even approaching that of the original muzzle-loaders. Their biggest mistake was that they kept trying to use the original hollow-base Minie-type bullet (or variations of it) which of course was less than bore diameter to facilitate loading from the muzzle. Such a bullet works as intended in a muzzle-loader - i.e. the skirt is free to expand at the instant of detonation of the powder charge, to engage the rifling right from the start. However, when the same type of bullet is confined in the mouth of a cartridge case, it cannot readily expand until the rear edge of the skirt has moved forward of the case mouth, which is really too late with black powder, as the pressure is already dropping by then.
However, keep in mind that all this was happening at the very dawn of the age of standard-issue breechloading military rifles, and they were really groping their way in the dark, so to speak. Present-day knowledge (gained from at least a century and a half working with breechloading firearms, don't forget) makes it seem obvious that the bullet used in a breechloader should be greater than bore diameter, of course. And that is the single most important bit of knowledge for getting acceptable accuracy from a Snider - though they can still be mighty finicky. Even though I can achieve much more consistent and satisfying accuracy with my Martin-Henry rifles, my Sniders remain 'dear to my heart' because of the very long period of their use as the primary-issue military longarms of Canada - from 1867 through 1896, when the "Long Lee-Enfield" (Rifle, Magazine, Lee-Enfield) was finally adopted by Canada. (As it was, not all Units had their sniders replaced until about 1905!) Although the rest of the British Empire for the most part switched over to the Martini-Henry beginning in the early 1870's, Canada's government decided that the Sniders were "good enough", and never did adopt the Martini-Henry (though a few thousand were obtained, albeit issued only on a very limited basis if at all.) Attached (third photo below) is a composite image of my Canadian-issue MkII* three-band Snider-Enfield rifle against a backdrop of the Fort Henry Guard volley-firing their Sniders ....
