True, I was leaning towards the 1204 states, but Magnum's suggestion fits the bill, however I think that it would take more explaination than a handwave to have the Ottomans allow Trebizond to continue to exist. Morea is slightly more plausible, since they can potentially play the Ottomans and Italians off one another until they have an established niche or the Ottomans begin to fall apart, but Trebizond won't have that until Russia becomes a power in the Caucasus, which will be some time, and I have my doubts that they can just keep throwing beautiful women at the Ottomans until the 1600s.
Avitus,
Do I sound that I mean a...handwave? the Ottomans started very small when they placed themselves almost in Galata while Constantinople was suffering from civil strife and managerial chaos;It was the Byzantines who allowed their progress and not the ability of the Ottomans.(con)
Here we are talking about a very powerful Nicaea,a healthy Trebizont,that in common cause they will dismantle these small seljuk principalities that are by and large in a period of confusion,to put it mildly.Both states will expand their holdings in Anatolia(among many other things) and when the Ottomans will appear later(1300) they will have to meat a very different state of affairs and will be too weak to face.I haven't mentioned here an intended alliance with the Mongols of Nicaea and Trebizond as well as Epeirus.
Bear in mind that the seljuks can be driven out of Anatolia and many can be christianised(or rechristianized for some),both christian states will have augmented population improved and sofisticated veteran armies and bend on expansion.
I understand that we speak about powerful states capable of surviving in the 21st century,not turkish vassals that became independent from turkish nomads who had the incredible luck to face a group of weak seljuk Beylicks,a weak Byzantine empire,west in turmoil and the near east embroiled in introverted bickering.(some times history sounds like an AH turkish wank...)
So the challenge you have Avitus is that you have to progress Nicaea which wiill be confined to Asia mostly(save certain European islands) with Trebizond IN ALLIANCE to extend in all Anatolia and Georgia in the next 100 years and exterminate an insignificant bunch of nomads under Osman(probably) being allied to the Mongols,Nicaea stepping south to Syria for conquests and a Michael destroying the latins and and bulgarians ariving outside Constantinople,you decide who conquers it,and go on from there.
Don't forget that these four Christian states have to act in close alliance if they want to survive and arrive in present time.
and about someone mentioning D'Anzou I will ask him to recall the Sicilian Vespers and the fact that he he might be willing to face one not three states against him.