Hi.
I originally went down the road of the Springfield conversions that were were made in Belgium and supplied to the Ottoman/Turkish Army. However, that system (referred to as the Poilvache) is different looking, although broadly copying the Snider system. As you say, they also have Belgium inspector's marks and Turkish stamps. They are uncommon, but turn up now and again. Also, the quality of the machining on the Watertown is much better than the Belgian models I have come across and I haven't found any other country marks on the rifle.
The British Snider-Enfield conversions look more similar, although the retaining clasp lock wasn't added till the later models. So, again, I originally thought that the Watertown had been converted after 1866 in Britain. However, if you compare the catch lock, they are quite different to the British examples. Also the ramrod is typically American, unlike the Enfield model. The Snider trademark logo does appear to be different to the British examples, but that doesn't prove it is an earlier version.
Finally, we come to the Roman numerals on the breech block that match the barrel ones. I may be wrong but I read that Roman numerals were used by Civil War period American gun makers to match assembly parts, where interchanging them wasn't possible. Also they were used if a weapon needed refurbishing and alterations. Is this the case?
Kind regards
John