*sigh* Here we go folks, the ethnic nationalists have arrived.
Issue number 0: We are trying to assemble a culture map based on local majorities in different provinces, whereas you just brought ancestral ethnicity into this. By that logic, we might as well slap a Hittite label on Sivas and be done with this charade.
Issue number 1: Actually, Barbarossa is a perfect example of the devshirme system, which was indeed a blend of forced assimilation and slavery. Its purpose, however, was to staff the Ottoman army and governmental posts; its victims would almost exclusively show up in Istanbul, the remainder in other cities and whatever forts, and it would not for the most part affect the tax records or the cultural makeup for rural provinces. I'm not even sure they taxed the devshirme, considering they were already de facto slaves on government payroll. Also, you can't just say the devshirme and their descendants count as one of the minorities (nor can you say they count as Turkish, for that matter), what with culture and racial origin not being the same bloody thing.
That is not to say assimilation and massacres did not otherwise occur in the Empire, but for the most part those happened during conquests and revolts, the former mostly predates and the latter mostly postdates the 1444 start date we are trying to establish population figures for. That last sentence segues almost perfectly into:
Issue number 2: I'm certain all of us here acknowledge the horrors of the Armenian Genocide, and all the other disgusting massacres and the highly volatile inter-ethnic relations in the region starting in the early 19th century. If you haven't noticed, however, we happen to be talking about what those figures might be like in 1444. That's 350-450 years before what you are talking about. We've already elaborated on how and why these figures would have changed, let's start with immigration (both in and out of these provinces, both Armenian/Greek and later on Turkish immigrations to the east from the Balkans) and proceed to... oh right, ethnic violence and genocide, and let's finish on differing population growth between different ethnic groups.
It's interesting how you also gave different figures for different data while trying to come up with a number for the Ottoman minority population in the 1900s: In 1900, the Ottomans still had a significant portion of the Balkans under their control. Despite them losing that land afterwards, the 1914 censuses seem to show a population of 18m, and I'm assuming they were downplaying the minority population so by all rights the figure should be higher. Then there were 2 genocides and a World War, and a quarter of the population of the Ottoman Empire as a whole died during WW1. So no, you don't just get to draw up minority ratios by dividing the number of minorities in 1900 to the population AFTER WW1.
Issue number 3: We are in fact completely certain Anatolia was not even close to being 100% muslim and turkish in 1440. We can in fact be completely certain that it never was and never will be that. First of all, reminder, this is based on the majority/plurality population in any given province. As for your objection to using the Muslim demographics from the census data, we indeed don't have any indication of what the Kurdish/Turkish ratio was in which region all the way until the 20th century. If you wish to argue for Sivas being flipped to Kurdish, let's talk about that. On the other hand, it doesn't matter whether the Muslim numbers represent Turkish or Kurdish or Turkish+Kurdish, when we are trying to ascertain the population of Christians in the provinces. Did the Pontic Greeks eventually end up bi-religious by the 1900s, yes. Were they the majority outside of Trebizond, which for all intents and purposes was the Pontic equivalent of Cilicia in that it wasn't conquered until 1460, that is somewhat more doubtful.
Issue number 4: You can claim that the Ottoman tax records are unreliable (though certainly indicative), because they only counted households at the time. You can also claim that a portion of the population converted religions without being assimilated, I would however expect this to not have happened in significant enough numbers for a few centuries yet. I'm not sure about that, sources from any side is welcome on this. In fact, I'm having trouble finding any studies whatsoever on the ethnic composition of the Ottoman Empire before the 1800s, because that's when everyone started to pay attention. Also, I find it odd that the tax records are our only source, do we not have church records for the population figures for the Christians around this era? Someone should look into the Mormon archives. Anyway, what you really can't say, is that we can simply disregard our one source the Ottoman tax records as unreliable. One, do you really think an empire whose only concern with its outer territoires was that everyone paid their taxes, would be so easily fooled by people lying about what they ought to pay in taxes? People actually converting, sure, people trying to trick the government, not so much. Tax records are quite often the most accurately kept document in any governmental institution. Or do you really think the Ottomans wanted to downplay the number of the people it could extort for higher taxes, because somehow it knew in the 1500s that rampant nationalism would be a thing and people would check those records?
Things I agree with: Kocaeli should probably start with a Byz core, if Paradox is actually considering giving Byz any cores, Sivas could be Kurdish, and we should look into the tax data for Cilicia around these times. Cilicia being conquered by Timur with lots of tribal incursions into the region, and reports of an Armenian exodus from the region with unspecified numbers, make me think that it could have been either way in 1444. What should be noted is that by 1900, the number of Armenians in northern Cilica was 40% according to European (so probably not biased towards the Turks) sources, and considerably lesser in the rest of the province. So yes, the Armenian population extending up to Erzincan seems to be the most likely analysis.