The Byzantines did a lot of large-scale population transfers within the empire to put minorities in useful places, accomplished both by encouragement and by force. Armenian Cilicia got its start in just that fashion. One possible way of creating an "Armenia" in another, more strategically viable location is simply to come up with a reason as to why a Byzantine Emperor would decide to move a whole lot of Armenians there. That might be cheating, though.
One possible way to aggrandize Armenian Cilicia a bit might be a dynastic union between Cilicia and Antioch, such that a prince of one manages to inherit the other and make good his claim. They were, after all, frequently allies. Antioch-Cilicia is not exactly superpower material, but it might qualify as an independent regional power given some reasonably proficient leadership and a flexible interpretation of the phrase "regional power."
What about, say, simultaneously with Cilicia growing in power and territory, the Byzantines manage to simultaneously push east as well, where they essentially create a buffer state in the Armenian Highlands that is loyal to them, while Cilicia proper tends to beholden to the Crusaders? Perhaps have it falter a bit to the Mongols, then come back as the important state that controls the passes west and east. And, with all of that done, Cilicia and Upper Armenia eventually reunite during modernish times under nationalistic forces