As I said earlier, the Ottomans have the best chance of the three to survive, just get rid of the Young Turks, and I don't think they'd survive in power without WW1.
Austria- Hungary; Remember before WW1 the Czechs and the Galizian Poles both wanted to reform the Empire rather than seek independence. In the war soldiers found themselves under officers who only knew German (a language the soldiers didn't necessary master), and many people wondered why they fought for a "foreign power". With Franz Ferdinand in charge, a reformer who had slavic symphaties the empire could survive, but would probably have to reform into a federation. I see more problems coming from Budapest, as the Magyars would be against any reforms that threaten their "special status". I could see Hungary becoming virtually independent (only way they'd agree) and Austria- Hungary being reformed into a federation consisting of Austria (including Slovenia and Trieste), Bohemia, Galizia, Hungary (the kingdom) and Bosnia- Dalmatia. Further Croatia would probably be in a special federation with Hungary. But I agree, if Franz Ferdinand's reforms fail the Empire would probably fall.
Russia; This is hard, there are several movements that want to topple the monarchy, as well as ethnic groups dreaming of independence. Russia would need a reformer to survive, but with Nicky II... things look very bad.