Is it wrong for me to have considered the turks our arch-nemesis since day 1?
Personally, I don't think there was ever a chance for a good peace in this timeline, until the turks are physically too weak to consider attacking Greece. The problem is that with Greece being this successful, it's frighteningly easy to just blame all of the problems of the Ottoman Empire on those damn greeks. And as long as there are greeks living in the Empire, the greeks will want to keep "freeing their brothers".
If the ottomans decide to remove the greeks, genocide, that will cause pretty much infinite bad blood between the two countries. At that point I wouldn't be surprised if there is some sort of ww2 style war of annihilation between the two sides.
Now on to the concern of turkey inevitably having a higher population than Greece, while that is likely, it's not certain. Slice off Kurdistan, losing lands north of syria, much larger Armenia, no Pontus, no straights area, no Thrace, no aegean coast. There's even more they can lose, if you consider Cilicia and any sevres style European exclaves. Turkey is a country that is pretty easy to rip off it's borders. Such a country would mostly be related to highlands and drylands, while lacking most of its coast. If a country like that surpasses Greece's population, then it must have sub-saharan African level birthrates, and probably a similar level of prosperity.
I would not be concerned about that country hating Greece.
Basically I think there's a 2 critical points. There's the point where you take so much land from the turks they never forgive you, then there's the point where you take so much land from the turks there's nothing they can do about you. I think once you get to the first critical point, it makes no sense not to just strive for the second. Because you don't want to be faced with a competent arch nemesis, most would prefer a crippled one.