Italian nationalism has already been successful: Lombardy, Emilia, Romagna, Tuscany have been annexed.
The reform of the Austrian military is somehow unlikely: the lack of effective generals, the incapacity of breaking the aristocratic rules and the lack of money to pay for everything (which is not going to get better after loosing Lombardy) will not go away, nor will their superciliousness. There is also Prussia, who is preparing and will come up for a knock-out match in the 1860s. Note that neither in 1860 nor in 1870 Austria was very much interested in making an effort to preserve the papal states.
A surviving Napoleonic regime is a pipe dream: Louis Napoleon is no more the man of the 1850s, and his diplomatic games in the 1860s were all failures. By the end of the decade he's going to be a sick man, and his regime is even sicker than the emperor. In this case too, Prussia is looking from the farther side of the Rhine.
The papal regime is not going to reform, not for a long time, and if the temporal power is prolonged it will be even worse.
How many divisions has the pope?