I largely agree.
But I think you might be overestimating "Turkish" as an identity in the first half of that period (or about 1131-1200) I think you'd almost definitely see a different culture than with an earlier reconquest, but different in the sense of details, not necessarily Greco-Turkish.
I think a Greek dialect that borrows a lot of words from Turkish and Persian would be a good illustration of what it would look like - if the Byzantine influence on the interior of Anatolia is strengthened, not weakened, in the 1180s and 1190s. Because if the Empire isn't seen as a place to turn to in that period -by those Turks who are concerned with models of "higher" civilization - they're going to look eastward like they did OTL.
http://www.iranicaonline.org/articles/saljuqs-iii Just as an interesting article, as it talks a little about Turkification of Anatolia.
So maybe I'd write it like this. If up to 1131 it could be recognizably the same soup, 1131 to 1200 is the same soup with a couple different ingredients and 1200-1264 is increasingly "You can call it calm chowder, but there aren't a lot of clams in it. And it doesn't look like its a chowder, either." - if that makes sense.
That makes sense and I agree. I should have been more nuanced earlier. During the early middle period, say 1150, the result would be significantly more Greco than Turkish, while a late date, say 1250, would have much more of the Turkish. My main argument was that by 1131 or thereabouts enough Turkish elements would remain after a Byzantine conquest to warrant the label Greco-Turkish, whereas beforehand not enough would survive to merit the 'Turkish' part.
But I will admit to not having a sound definition of the difference between 'Greek with some Turkish bits' and 'Greco-Turkish'.