It would seem that there was not much direct export of (military style) European guns to the various regions till closer to the end of the Ottoman Empire. Especially during the years you posted interest in. The few remaining specimens with appropriate marks on their lock plates or stocks would indeed indicate government ownership at some point. Another problem is that the Ottoman Empire kept very little written records of their gun building, testing, usage, etc. Unlike Europe with it's large arsenals, most of the guns from this period were assembled in small shops scattered across much of the Empire. They had their own style of guns they preferred, which were essentially the same as civilian guns. In fact, they continued the use of the flintlock all the way through the 3rd quarter of the 19th century. Which is the likely reason so many examples still exist today. These small shops must have numbered in the hundreds. Even entire towns and villages were devoted to arms making. Often under contract to the Ottoman Empire. But it is well known that large numbers of locks and barrels were exported from Europe for sale/trade to all of these regions for local assembly and stocked and decorated to local tastes.
Rick
