You know, this might be a bit more plausible than I originally thought at first glance. I might be talking out of my ass, but wouldn't the willingness of all three parties (plus Georgia, Meso, and possibly an independent or semi-Despotic Khazaria) to settle the borders depend on how important the current incarnation of the Silk Road is for each? Other than (increasingly diminished) overland trade routes and whatever big cities exist in Central Asia, there's not much to really risk a global war for. For that, you can thank the rising and established powers in Mexico, Japan, India, and Island Asia. The Eurasian commercial networks, I think, have generally shifted southwards in a way that access to the Indian and Pacific Oceans for those three empires specifically is what matters. Unless the Ottomans place an unreasonable premium on maintaining their control over the porous deserts and steppelands of Central Asia, we may very well see a quick drawing of borders after minor skirmishes that ends with Russia becoming responsible for everything north of the Jaxartes, the Ottomans getting the good bits south of it.