Ottoman censuses began in the early 16th century.
I'll refer you to some of
Chamboozer's old posts which I dug up on the matter regarding the specifics/sources, since he's an actual expert on the matter whereas I am not. If those don't satisfy you and you really still want me to find some academic works covering it, I'll try to look up the ones I found last time this subject came up.
"The Ottoman census records show that the regions were predominantly Turkish at around the start of the game." Thats what u said.
First, Chamboozer talked about Izmir, right? He refers to the dissertation by Olnon. I would like to note that its about 1 city, not the rural areas, not the other cities surrounding Izmir.
"Accurate demographical data are not available for the bulk of Ottoman territories prior to the first modern Ottoman censuses of the 19th century. This has posed considerable problems for socio-economic historiography, but these have been partially overcome by the creative use of Ottoman tax registers (tahrir defters). Unfortunately, the inventory of the tapu tahrir-series (abbreviated as TT) in the Ottoman archives lists few such registers for the 17th century." p. 47.
The problem u and Chamboozer have is that u talk about regions while the "tax registers" only reflect the towns ethnical composition.
"The other example, which I know rather better, is Western Anatolia and in particular Izmir." thats what Chamboozer said. Cut the first part and only leave "in particular Izmir" and i agree.
Nonetheless i wouldnt want to change EU4's current cultural situation In the province Izmir. I just wanted to point out the urban/rural disparity and the lack of rural census.
The migration theories which use certain events as the conquest of timur for its explanaition are on my opinion only speculations.