Don't know about Christian solidarity but
if you ask how the Ottomans managed to emerge from the mess of c1580 (death of Grand Vizier Mehmet Sokullu) to c1650, it was quite straightforward.
Mehmet IV came to the throne in 1648 (aged 7); his mother was a strong-willed woman, Turhan Sultana.
His grandmother was the wicked witch of the East, Kösem Sultana, who had ruled through the reigns of 4 sultans (essentially bumping them off when they got too uppity). Fortunately, Turhan arranged her demise in 1651.
(This would make a good I, Claudius-type series, I guess).
Turhan was OK, but no rocket scientist. In 1656, Mehmet Köprülü became Grand Vizier, on the condition that he would enjoy absolute power. The fun-loving Mehmet IV agreed. Until his death in 1661 Mehmet Köprülü instituted a reign of terror that seemed to restore central authority. In 1661, his son, Fazýl Ahmed Köprülü became G.V., and he was a better administrator, restoring balances and reforming the army and navy. In 1676 he died, and another Köprülü, Merzifonlu Kara Ahmet, became G.V. He too was a very good administrator.
But then came the siege of Vienna. Both the G.V. and the Sultan were murdered.
And the Ottomans began their long and increasingly ugly decline.
