I am not sure if this will be helpful to you, but it may at least be interesting to you and some other members.
Have you ever heard of the differences between "Interchangeable Pattern" (IP) Enfields and "Non Interchangeable Pattern" (NIP) Enfields of this period? To make a very long story somewhat brief, the British Government stipulated that P1853 through P1861 Enfields for Government Service were to be of the IP, once that manufacturing capability became available at Enfield Lock. Of course, these arms were more expensive to make than the same arms that were not manufactured to Interchangeable Parts tolerances. Both British and later American Contractors made the less expensive Non Interchangeable Pattern Enfields for those who did not wish to spend the extra money for Interchangeable Parts Arms. To give an idea of the difference in price, IP Enfields were purchased by the U.S. for around $22.00 - $24.00 while NIP Enfields were purchased for between $17.00 and $19.00 during the WBTS.
OK, so what has this got to do with your Rifle? Well, since your Rifle was almost certainly not a British Ordnance approved/purchased arm, the barrel and lock are probably not (though not certainly) Interchangeable Pattern Parts, so they might or probably not be a "drop in" fit into an original Interchangeable Parts Pattern made Stock.
Back in the 1973 and off and on for many years after when the Marine Corps did not have me stationed too far away, I worked as an Artificer/Armorer/Gunsmith at was then called "The Navy Arms Booth" on Sutlers' Row at the North South Skirmish Association Spring and Fall National Championships.
In the early 1980's when Navy Arms was still importing and selling the REAL UK Parker Hale Enfields that were made on the Interchangeable Parts Pattern, we carried a wide selection of parts, including spare stocks and barrels. One day a Confederate Skirmisher walked up to our booth and asked if we had any original P 1853 barrels that were in good enough condition to shoot in the competition. Much to our surprise, he had an almost complete Original Tower P1853 Enfield including the barrel bands, but missing the barrel. (He had purchased the parts that way and did not know why the barrel had been removed, even though he had asked.) We did not have any original barrels, but we noticed the “Tower” marking on his lock as well as the Queen’s Cypher and Broad Arrow markings. We informed him we did have brand new Parker Hale barrels that might fit with little or no work, though. He decided he wanted to look around for an original barrel, so we wished him the best of luck and off he went further on Sutlers’ Row.
About 2 or 3 hours later, he returned and informed us he had no luck finding an original barrel and inquired about the PH barrel. We informed him we would be happy to see if the barrel fit in his stock and if it did not, there would be no charge. Much to all our surprise, that barrel hand pressed into place as nicely and solidly as if it had been made for this stock 120 years earlier. We also supplied a reproduction PH Tang Screw and in short order we screwed it and the barrel bands in place making it a complete gun. When he asked what the “gunsmithing” charge would be beyond the price of the barrel, we told him there was no extra cost and we were well pleased it fit so nicely. So off he went gleefully to the firing line. He returned the next day and told us the Rifle Musket shot much more accurately than he was able to hold and thanked us again. We thanked him for learning something we only suspected.
Now because your Rifle parts may or probably are not of the Interchangeable Parts pattern, I cannot guarantee they would be a “drop in” fit in either a REAL UK Parker Hale reproduction stock or an Original Stock of the Interchangeable Parts Pattern. However, if you run across either of those stocks, it may work or be able to work in such a stock with not too much fitting. Just something you might be interested in checking in case you ever run across either kind of stock.
Now, I can say that I would not expect an Italian Reproduction stock to work well with your parts, because the shapes of their barrels were different than PH and Original Barrels. However, with some inletting and glass bedding, such a stock probably could be fitted. OR using glass bedding, you could tighten up the fit of your stock to the barrel, in case you would like to fire the Rifle. Now of course I would recommend having a qualified gunsmith inspect your barrel and breech before you would fire it, though.
Gus