The example you give as type 2, if you intend to offer that an analogy to unity among the Orthodox, is crude at best. Unity among Orthodox bishops is more than teaching the same things (although that should never be trivialized or downplayed, since the Church has always held that teaching and believing the truth is of great importance) and having cordial relations. Unity among Orthodox bishops is about sharing the same Eucharist (the body and blood of our Great God and Savior, Jesus Christ), which, to quote a Catholic teaching, is “the source and summit of the Christian life” (CCC 1324). There is no form of Christian unity that is more significant, or actually more unifying, than that of Eucharistic sharing.
As far as your not wanting to hear of your “type of 2 unity,” may I ask why you persist in this discussion? One does not enter into a discussion with others, proceed to dictate to them which arguments that may and may not us, and call that an honest debate or discussion.
It has repeatedly been explained to you what are the Orthodox bases for unity: shared faith in the same God, who is Father, Son, and Holy Spirit; shared submission to the same authorities (God, the tradition of the Church, which includes Holy Scripture, the Ecumenical Councils, canon law, and the hierarchy of the Church), and Eucharistic sharing. There is no Orthodox version of the Pope of Rome. In other words, there is no one bishop with universal ordinary jurisdiction. All of the bishops of any given Church are subject to synod. The synod itself is routinely the highest merely human authority within a particular church, although a universal council of the bishops would exercise a higher authority.
It is fine that you believe that the Orthodox lack something by not being in communion with the Pope of Rome. As a Catholic, it is expected that you will believe that, since that is Catholic teaching. However, it is a different matter altogether to move from that position to saying that the Orthodox lack visible unity. To put things bluntly, that position is absurd–from the Catholic point of view, since the Catholic Church itself considers the Eucharist to be the source of Christian unity (see CCC 1322-1327, 1348, 1352, 1369, 1396, 1398, and 1418), even saying that “the Eucharist makes the Church” (CCC 1396).
Orthodox generally understand that one particular aspect of the Catholic approach to ecclesiastical unity involves the Pope of Rome as the principle of unity. Although they do not believe union with the Pope of Rome to be essential, and they do not have a bishop who has universal jurisdiction like the Pope of Rome, I think the only sort of Orthodox who would say that the Catholic Church lacks unity because the Catholic Church’s approach to unity is not identical to that of the Orthodox are those Orthodox who either don’t understand Catholic ecclesiology, or who are anti-Catholic bigots.