When would have been the moment when this would have been:
January 1878 would be the date, the Russians were at the gates of Constantinople, but their advance had been stopped, their effort plagued with bad logistics and bad luck in general, they were forced to the table in a rather disadvantageous position, at the time the Austro-Hungarian Army wanted to join Russia, but the Austro-Hungarian Diplomacy didn't want to be on the bad side of Britain, nor compromise permanently its relations with Turkey. If other more hawkish faction had the power at the time Austria could have tipped the scales in favor of Russia enough to participate in the carving of the Ottomans. The alliance of the three emperor would probably survive for more time, but Britain's reaction and how the Austrians and Hungarians would deal with the sudden increase of people is everyones's guess.
Austria should at least demand Serbia, Montenegro and Bosnia in the aftermath.
What about Romanians/Vlachs? Their independence OK, or must they be added to the deluxe Habsburger or partitioned a Polonaise with the Romanovs?
If not outright annexed they should never be allowed to unify and be kept both as protectorates of AH, but it would be better if they are kept inside, it is always good to have more of the Danube.
Bulgar and Greek independence harmless to Austria, eh? What about Albanian?
Bulgaria + Istanbul/Constantinople as a Russian Protectorate, to satisfy them, even better if Bulgaria becomes a multinational state. Albania should be a protectorate or heavily dependant of Austria, because their coast could be used to block or harass Austrian shipping leaving the Adriatic. Greece fully independent with OTL 1914 borders would be ok, if kept neutral or friendly to Austria.