Eurofed
Banned
No Italian guaranteed neutrality (since Nappy will never agree to give up the Pope) and firm opposition by the Hungarian half of the empire, but Austria still goes into the war? Even assuming that they don't know about the secret Prussian-Russian compact it is a tall demand.
Well, they didn't know about it, precisely because it was secret.
There are just two ways I see it possible: an assassination attempt against Franz Joseph mounted up by pan-German circles (or Italian irredentists) or Bismarck making up his mind and deciding that the Austrian question must be resolved in 1870. The latter is certainly almost ASBish, but I'd say that both are quite unlikely.
Agreed about the implausibility of the latter, but the former is not unlikely at all, since an assassination attempt by an Italian irredentist on Franz Joseph's life took place in 1882. We just need to anticipate this by a decade and half, not difficult at all (especially if TTL Italy did better in 1866).