Okay, I'm sure somebody who knows more about this particular corner of history could correct me and complicate the admittedly overly simple process I'm predicting, but I think I have an idea about how this could happen.
For whatever reason, ramp up the level of involvement the Kievans/Varangians had in the Eastern Roman Empire and have it stick around for a while longer than OTL.
Two things happen as a result of this:
1) In the eventual Rus' intervention against the Bulgarian Empire becoming a threat to the ERE, the Rus' win conquest rights over much of the Pecheneg lands and control over the mouths of the Dniester, the Dnieper, and the Danube.
2) On the other hand, the wars the Rus' DO have against Byzantium are far more destructive than OTL, and both the Normans and the Arabs make headway while the Roman Navy is tied up in the Black Sea. The Empire is under pressure on three fronts, and is experiencing internal instability as a result.
So, it's likely that there's breakdown in the agricultural supply train (for the Romans). There is some internal migration over the decades within the ERE, from the raid-prone Anatolian highlands down to maritime cities on the Aegean. On top of that, frequent exposure to raids from the more navally-minded than OTL Rus', Pechenegs, and Bulgarians bring plagues which devastate cities in Anatolia and stem the tide of invading Arabs and Turks in the east.
Eventually, the Byzantines bow to Rus' demands and invite them in as a defensive force, much as they had before the Rus'-Bulgarian war, which ITTL ended with the Rus' holding Constantinople as a means to get recognized control over Thrace and the Danube delta. This officially begins the start of a Rus'-Byzantine relationship that bowed heavily in the Rus's favor. The Rus' lead major raids against the incoming Turks, which have been pent up in Persia for two centuries longer than ITTL and have subsequently assimilated and become more powerful as a result of control over Persia's manpower reserves. The fighting is fierce and lasts a century, and depopulates many of the border towns. Armenia gains power in the Kurdistani region, and eventually, by becoming structured and seasoned enough to drive Turkic raids out of their territory, creates a geographic bottleneck for Turkic forces to enter Anatolia. Supply lines over mountain range where every tree or hillock could be concealing a raiding force eventually force the Turkic states to give up. Rus' control over Anatolia is acknowledged by the ERE and informally recognized by the Turks, and a long and steady period of Russian settlement in Anatolia begins.
There's my scenario, have fun speculating on all the butterflies you'd get from it!