In the long run It ends with the end of the eastern roman empire.
Those defeats did hurt the greeks, but it also paved the way for some very serious reforms that finally ended the constant series of civil wars and allowed them to rebuild after a series of mistakes. It also made the Islamic world over confident, in their own invincibility, so they didn't notice as much when the christians reorganized, as they got stronger as they learned about the value of logistics displine and slowly regained Antolia. Slowly reconqured spain, and when the great disaster of the mongol invasions came they shattered like glass.
The failure of the first crusade, of the second crusade, paved the way for a resurgent europe for the victory of the third crusade, the reconquest of Egypt and the slow reconquest of north africa, by the time the Islamic world had recovered from the Mongols from their collapse the mediterarian had once again become a christian lake.
Their attempt to cut off the christians from global trade would back fire in 1492 with Columbus making his famous voyage.
The wests current dominance is due to that nessary and vital favor, with out that defeat our positions would switch and North africa would remain muslum, Antolia would have been conquered, and the whole of europe would have fallen in time.
OOC: Columbus and the Mongols wouldn't exist with a POD in the 11th century. You also seem to be kind of ignoring the OP, which actually rules out a conquest of Egypt.
IC: Those are some pretty intense fever dreams, but also not unexpected from Romanophiles obsessed with the old
renovatio imperii card. In fact, the "Roman" revival in the 12th century can be attributed almost entirely to Nikephoros III Basilakes successfully revolting his way to power on the backs of Slavic and Frankish mercenaries. Rather than appeal to the Pope, he introduced the idea that Norman mercenaries could be the counterbalance to the Turkmens. It worked well enough in the 12th century, I suppose - I mean, they did manage to get most of Anatolia back. Your call if it was worth the tradeoff of the Frankokratia once the Normans decided that they controlled most of the land in practice and thus should have a say in picking the Basileus. Needless to say that most histories consider "glorious Rhomaion" to have ended when Guy of Giberville and his army sacked Constantinople and assumed the purple by force, which gave us the joyful little bundle of nonsense that is the Latin Empire.
Mind, the Latin Empire did have a pretty good run, but most of their conquests were undertaken by independent Greco-Normans and turned out to be fairly ephemeral, particularly the short-lived Norman capture of Alexandria - that lasted, what, five years? Seven? The Duchy of Africa held out the longest, sure, but by the 14th century it had been swallowed up by Berber rigorists. It's certainly a testament to the endurance of the Greco-Normans that you can still find communities of them living in coastal cities like Mahdia and Tunis.
The "Christian lake" period doesn't refer to the elimination of Islam, it refers to the trade dominance of Genoa and Amalfi during this period. The fact that you could find Genoese merchants in most ports in the Arab world doesn't mean the Mediterranean world was Christian, it means Genoa won the trade wars at the time.
I wouldn't say that the Muslim world "shattered like glass" when the Mongols arrived; even referring to them as "the Mongols" is a misnomer. For one thing, there weren't that many of them, and they migrated in dribs and drabs ahead of the Tangut invasion of Rus' - they came at the individual clan level, not as a unified whole. Some Muslim states certainly used Dughlat and Naiman warriors as extremely potent
ghilmans, notably to flatten the Norman Principality of Cilicia. But "the Mongols took over" is a gross distortion based on Khagan Unegen and the rest of the Ebugedjin clan knocking over the Turkmens and taking their place as the effective sultans in Persia and Mesopotamia. If anything, Unegen - and of course his son, Abu-Bakr - stabilized the Muslim world for awhile under the Ebugedjin Sultanate.
Not sure why you're bringing up Sancho Colombo; his land voyages from Cordoba across the world were impressive, and
The Fantastic Voyages of Columbus is certainly worth a read just to see one man drift his way from Leonese Cordoba to places as far away as Tekrur, Yemen, Suomi and even China. He definitely got around. But he's also just describing trade lanes that already existed.
Of course, by the time those sailors from Bristol discovered the West, the Latin Empire wound up blowing up into a bunch of feuding principalities, half of which converted to Armenian Christianity for some reason?? *shrug*