If you already Greek, change faith to Orthodox. And you can form Byzantium and get it cores.
It's certainly an option, and one I considered at the start. There little point in doing so now just to get cores on Naxos, Cyprus, Crete, and Kaffa.
There's a couple of problems with taking this route as the Knights, however, aside from the most obvious - why play the Knights to form Byzantium, when you can play Byzantium and re-create the empire in a fration of the time it takes you to conquer a second province as The Knights.
The first problem is that in order to succeed as The Knights, you need to become a trading power. Infamy gives you a significant penalty to your compete chance, and if you get too much infamy your economy will tank (8 infamy, the full cost of annexing a 1-2 province minor, was enough to cause me to lose all my merchants in Lubeck, the largest CoT, even with full free trade and both trading NI's.) To form Byzantium, you need to conquer Greece. Greece will likely be owned by Christians and Orthodox countries, which will probably be infamy intensive and slow going. If Greece is still owned by the Ottomans, it probably means they're too strong for you to take on. It's usually far cheaper, infamy wise, to expand against the Muslims and Hordes in Anatolia.
The second problem is that in the long run, staying Catholic is a stronger option. Once you convert Anatolia to Catholic, you start to have a decent chance of becoming Papal Controller. If you can carve up the Balkans into a number of small states, you can force convert them to Catholic, then annex them later via excommunication wars for low infamy. Being Papal Controller also saved me from facing a combined Austria/Bohemia mega-blob.