I know that when the Alexandrian and Antiochian Patriarchates fell into heresy, Orthodox Patriarchs were elected.
I think that's a different scenario all together. In both cases there was a dispute and division among the members of the Patriarchates which led, sadly to schism.Appointing an Patriarch in Communion with Constantinople was done to serve those who wished to remain in Communion with Constantinople. This is not the same case here. Although there are schisms and potential schisms among the Roman Catholics, none of the groups are in schism particularly to be n Communion with Orthodoxy, so in my view, it would be terribly wrong to appoint an Orthodox Patriarch of Rome.