I think the best departure would be the survival of the
Medieval Armenian state (not Cilician Armenia which was a successor kingdom) under the Bagratuni Dynasty. It was a major power by the 11th century. Unfortunately, the Byzantines worked against it and annexed it, only to lose everything after the Battle of Manzikert.
If for some reason, the Byzantines saw Armenia as a useful asset rather than a rival, Armenia would survive. We could then have a scenario when the Seljuks come, that the Armenians are able to negotiate with Arp Aslan who leaves them alone and the Armenian state remains intact.
When the Seljuk Empire breaks up, Armenia is able to take advantage and expands south and east to the mountains, blocking further Islamic expansion and incorporating the areas now populated by the Azeris and Kurds. It does reach the Caspian Sea to the east, and its border to the west could be anything.
The Armenian state has its ups and downs over the centuries, but basically is able to hold onto the lands of Greater Armenia. By the modern era, Armenia holds the oil rich lands around Baku and Mosul and becomes a major oil power. We could even arrange things so that it has access to the sea either to the Black Sea near Trebizond, or towards the Med by including Cilician Armenia and the port of Iskenderun.