Okay, let's look at the best case scenario for the Romans during the 12th Century (fun fact: the Romans aren't conquering Egypt; I mean, they struggled to hold on to Cilicia during this time, which was significantly closer to Constantinople than Egypt).
Starting with Alexios, basically the reconquest of Western Anatolia goes about as well as it could possibly go so no need to change this. The important PoD is that the Roman contingent under Tatikios chooses to remain at Antioch throughout the siege and at the end of it the Romans are rewarded with Antioch. This means the resources poured into taking Antioch from the Normans OTL can be poured into more important efforts, like the reconquest of the Anatolian Plateau. Of course, this doesn't happen over night, but without Alexios and John spending significant parts of their respective reigns dealing with Antioch, it means Anatolia receives the attention it deserves much earlier and much more thoroughly.
Which is the key. Like I said, the reconquest of the Plateau isn't happening over night. It's going to take decades of effort, involving almost yearly campaigns into the Plateau beating up the Turks, wearing down the Sultan's authority until it finally breaks and the Sultanate disintegrates into dozens of Beyliks. Before you say anything, this is entirely possible. It's basically what happened in the late 13th century (except it was the Mongols, not the Romans that did it), except now it happens in the mid to late 12th century.
From here the Romans basically do to the Turkish Beyliks what they did to the Armenian statelets in the 10th and early 11th centuries, basically working to plug the various Beys into the Roman system, and over time the Beys will begin to see the value of letting the Romans inherit their lands on the Plateau and retiring to an estate in the Balkans. It's a lot easier to live on a luxurious estate than it is to govern a bunch of unruly nomads.
It's a lot easier to do this to a bunch of small states than one big one. In short, the Romans would be creating a power vacuum and then filling in that vacuum with themselves.