Religius is good choice. Amongs others for lower culture conversion, since its obvius what it does. When i play as Cyprus i refuse to convert Greeks/Romans to Catholicism, because i feel like those guys suffer enough to be under Ottoman rule. Instead i keep Orthodox faith. Like you, if i understood wright, i tolerate Orthodox faith and Greek culture.I rarely live past 1650, but depending on the circumstances Religious - Naval or Defensive - Maritime or Espionage - Innovative - and then the Winged Ottomans arrive.
It would be nice if there was a nicer way of keeping the Orthodox island happy without raining gold and monarch points on missionaries and the "Greeks in the Order" decision since the Ottoman navy overwhelms mine even if they are at war with Venice and the Mamluks at the same time, but hopefully Emperor will finally give me a fighting chance. (And the opportunity of having a Highlander Grand Master...)
The only realistic way of expanding as the Knights as it is now requires you to prey on Byzantium, Venice and Cyprus as soon as the Winged Ottomans arrive, and if I make Byzantium my vassal (technically preferable to full annexation by the Turks, so somewhat forgivable, Rhodes aside) I would still be in a really weak position and with land directly next to the Ottomans. Not even Scotland and Brittany are that much surrounded, by thunder.
Perhaps try with Knights following ideas : 1. Naval, 2. Humanist, 3. Defensive, 4. Exploration - since crusader states are geting new mission tree, amongst others ''Knights of the New World'', where i presume you'll do colonizing and discovering Fountain of Youth. 5. Quantity, 6. Economic, 7. Quality and 8. Trade. Trade idea is realy one of the best to solve your money problems. And it helps alot. But again i say once you form Jerusalem and reach 7th idea Ottos don't have much chance against you in 1 vs 1. Also in one ocasion i secured Alexandria, created land conection to it, promoted Egyptians and converted them to Catholic. I builded Suez canal, where i let Ottos deplet themselves with my Forts while my armie are in Egypt, protected by my mighty navy and Suez canal. Basicaly all they could do was to attack my heartland, while not being able to cross Suez canal. Later on i ofcourse release armies of Crusaders to hunt them down and liberate the Holy Land and humiliate them. This is of course only game. I don't want to insult anyone.