I agree with all of those points except for the increase in population, but when they recover the Byzantines should push in Ukraine and Syria.If the byz can retake anatolia and hold Greece, perhaps Bulgaria then I see some of the following happening just naturally from this situation :
1 their power in the east forces a decline in venice. Veniceian wealth was based upon trade and perhaps parasitic usage of the ex byz state. A raise of byz means a decline of venice.
2 with the ottomans driven far from Europe. The byz should be vastly superior to eastern states as to gunpowder wepons. Same as the ottomans were in their great eastern conquests. So a natural expansion in the future into the middle east is a natural situation after they stabilize themselves.
3 population. The conquest of constanaople in 1453 relied upon substantial anataloian warriors. These same warriors were drawn from existing populations not new Turkish warriors. If byz owns anatolia many of these would be available for byz.
4 the initial ottoman state of part of the Balkans plus anatolia should provide the same power base as the ottomans had for their future power projection.