The key to being the Byz emperor was to have control of Constantinople. If you held this then your claim could be validated,... For a timeline like this you might wish to read :::
The Late Byzantine Army: Arms and Society, 1204-1453.. in there he talks about the conquest of Const. and the need to defend the provinces in Europe to the determent of Asia. The army was doing well in Asia and was at peace, in that the Nicean army could handle and defend the Turkish border. The conquest of Const. and the subsequent need to defend and fight Serbs, Bulgurs, & Europeans forced the Niceans to constantly denude the Turkish border. I think if you had had a stronger Latin state which defeats the other Byz pretenders in Greece -Albania would have focused the Niceans to expand east ward. This expansion could have encompassed the complete conquest of Anatolia plus more. From their to follow your timeline have the Latin kingdom deteriorate closer to the 1290 period and have the Niceans complete the conquest then, with stable eastern borders.