Nicholas holding onto the Russian throne is difficult, what if Anastasia had been born a male, say for the sake of the TL he is known as Tsarovich Peter, this butterflies away Alexei. Perhaps if we can kill Nicholas off sometime after the 1905 revolution, it would make the Tsardom easier to save. Grand Duke Mikhail, the brother of the late Tsar Nicholas II rules as regent while, the late Tsar's only son is crowned Peter IV.
Lets give Peter IV an inquisitive nature, he grows up wondering why his father was assassinated. He is often told by those in the Royal Courts it is because of anarchists who want to destroy Russia, or some other lame excuse, but Peter IV doesnt buy it. There is something terribly bad with the country and he wants to find out what.
Throughout the war, when things start going bad, there is alot of unrest in Russia, but most people blame Mikhail rather than the young Tsar. In a rather bold move, Mikhail is arrested by the order of Peter who believes he can now rule the nation without a regent, aware of the anti-Tsarist sentiment growing in Russia he bolsters his support by ordering members of the royal court onto rations giving food intended for the royal family to the people of St Petersburg, the army in the east takes a purely defensive stand, while the army fighting against the Ottomans takes aggressive measures, Trebizond is once again in Christiain hands as is Adrianople. With Britain and France as his allies now, he goes after Constantinople succeeding in taking and holding the city, shortly after the straights open up to allied transportation, allowing food shipments from the America's to enter Russia, when the United States enters the war, firearms pour into Russian ports and are sent to the front with Germany.
Faced against Four powerful nations, allied together, Germany surrenders earlier, before the Yanks see much action. France and Britain are concerned with a Russian Constantinople, but how far they protest it is up to speculation. Perhaps some sort of deal is worked out where the city becomes Greek, the Turks are expelled, forced to resettle in Anatolia somewhere. The straights become "Christianized" and "neutralized". Russia gets a warmwater port in Trebizond. Perhaps with the flow of Russians into the area of Pontus, the Pontic Greeks move westward to settle in Constantinople and eastern Thrace. Perhaps when Turkey and Greece do a population exchange it wont be determined by Christians and Muslims, but Turks and Greeks. Greek Muslims settle in Constantinople where they take over Muslim holy sites such as the Blue Mosque, while the Christians reclaim important places such as the Hagia Sophia and Hagia Irene. If not and the population exchanges go as per OTL, look for Turkish mosques to be converted to Eastern Orthodox Churches, Im sure the Greeks would enjoy not only reclaiming their cathedrals but converting mosques, the way they had to watch helplessly as it happened the other way around centuries before.
Alternatively the straights could become Greek, as does eastern Thrace, but Constantinople becomes an open city. Of course after Russian occupation, the aforementioned Christian sites will be reopened to Christianity, even after any peace is made to end the war. Constantinople will have many different quarters broke down probably into ethnic groups, such as the Turk quarter, the Greek quarter, the Russian quarter, the Bulgarian quarter, maybe an Italian quarter or Spanish quarter or someother Catholic group. The city will become one of the most diverse in the world, and while technically independent be a protectorate of the United Kingdom. I wonder how the government of the citystate of Constantinople will look?