Would this essentially be creating a knightly class in the Byzantine Empire? What about importing western European knights and their traditions with promises of land?
It would take way more than a Knightly class a la early Normans to achieve this: it would take a much more significant portion of the Byzantine population to create an equivalent to the Ghazi culture. It would still require the influx of more Latin and Turkish mercenaries at first to teach them the know how, then a reasonable percentage of the locals would have to adopt a lifestyle that frees them to train for war almost exclusively. That may be achieved in a few different ways:
A- They go the Frankish way, using the abundant pastures of central Anatolia to keep thousands of war horses, but use them mostly as troop transport for chevauchee raids, not necessarily in combat. They may fight the Hussar way if mounted, but mostly dismounted. Most of the warriors are also part time herders.
B-They adopt the nomad turkish lifestyle and become a kind of Byzantine Cossacks. They fight mostly as horse archers.
C-This is the least likely, but still somewhat viable depending on how realistic the timeline is. That is, the Byzantine emperors enslave or force a significant amount of people (muslims and POW maybe?) into serfdom and constantly harass them to supress any rebellion. A more humane option would be to make that serfdom an equivalent of Jizya tax and leave them in peace. What the latter produce would be used to fund an army of citizens. This would be similar to the Spartan Helot system. Sounds ASB, but it may be a very interesting timeline
That's why I suggested turning the Great Catalan Company into the founding stone of this new warrior culture as the fist step: those nasty motherf****** lived for war and booty only, specially the Almogaver infantry, and consistently destroyed turkish after turkish army. The timelime might then proceed like this:
Their commander, Mega Dux Roger de Flor is not assassinated thanks to listening to his wife and advisors. Instead, he finds a way to bring down his political enemies. He might not overthrone the Palailogoi. If he does, he can enthrone the former (and succesful) commander Alexios Philantropenos as the new emperor, or the Cantacuzenoi for that matter.
Together, they reform the political system in order to give Mega Dux De Flor power similar to a kind of Generalissimo or Shogun who can oversee the stability of imperial sucession and act as a counterbalance to the nobility. They bring in more Iberian warriors, including more Iight Jinetes that can train the new armies the way to go in the following wars, imbuing the populace with an Eastern Reconquista spirit. On occupied territory, allowing most nomadic tribes to fight for them without necessarily converting and learning from them too would be the next step. Any further conquest means land grants for the succesful commanders, similar to the Timariot ottoman system.
From then, the rock starts rolling. Depending on the length of the timeline and the level of WANK the author wants to implement, this new empire might grow to a size that may rival the old Roman Republic (but not necessarily the same territories).