St. Theodore the Studite is certainly an irregularity within the Byzantine tradition, but he's rather late if you're trying to establish the primacy of the Bishop of Rome as a universally held apostolic tradition.
St. Theodore certainly affirms said primacy, but he is far from an irregularity in Byzantium in doing so. St. Maximus of Constantinople, much earlier and very plainly, declares the Roman Church "from of old until now, as the elder of all the Churches under the sun, presides over all?" Saying that Apostles have established and Councils have confirmed this, he continues "she is subject to no writings or issues of synodical documents, on account of the eminence of her pontificate, even as in all these things all are equally subject to her according to sacerdotal law. He writes elsewhere that "from the coming down of the incarnate Word amongst us, all the Churches in every part of the world have held that greatest Church alone as their base and foundation, seeing that according to the promise of Christ our Saviour, the gates of hell do never prevail against it" (these citations in their historical context may be read http://www.newadvent.org/cathen/10078b.htm here). St. Theodore also tells us he is not repeating any personal opinion, but giving voice to the Tradition of his Church from the earliest times, "Order that the declaration from old Rome be received, as was the custom by Tradition of our Fathers from of old and from the beginning. For this, O Emperor, is the highest of the Churches of God, in which first Peter held the Chair, to whom the Lord said: Thou art Peter ..." (sources here http://www.fisheaters.com/easternfathers.html)
St. Maximus attributes to Rome a primacy according to "all the holy synods, according to the holy canons and definitions," the question is though: what synods and what canons are St. Maximus referring to? Also, this really doesn't help your case, since St. Maximus is implying that Rome's authority comes from councils.
Also, with regards to St. Theodore, if he's quoting from the tradition of the earliest times, why do you resort to quoting later Byzantine theologians who may or may not have been exposed to altered canons?
Among others in Constantinople, we have Patriarch John VI who confirms the Petrine privileges belong to the Pope of Rome, he says "the Pope of Rome, the head of the Christian priesthood, whom in Peter, the Lord commanded to confirm his brethren." There are many witnesses to this truth outside Constantinople, Metropolitan Sergius "O Holy Head, Christ our God hath destined thy Apostolic See to be an immovable foundation and a pillar of the Faith. For thou art, as the Divine Word truly saith, Peter, and on thee as a foundation-stone have the pillars of the Church been fixed" is only one. So, when St. Theodore tells Pope St. Paschal, "Hear, O Apostolic Head, divinely-appointed Shepherd of Christ's sheep, keybearer of the Kingdom of Heaven, Rock of the Faith upon whom the Catholic Church is built. For Peter art thou, who adornest and governest the Chair of Peter" he is only confirming how the Church of Constantinople always traditionally understood the Petrine passages in Sacred Scripture.
That last bit is a bold (and blatantly false) statement when you consider that St. John Chrysostom was once Archbishop of Constantinople.
The "false translation" or misinterpretation claim in St. Ignatius or St. Irenaeus is unsustainable. Regarding the passage in St. Ignatius, you would have it reduce to a tautology, Rome presides in the region of the Romans! But the meaning is "To the Church which presides, in the region of the Romans, ..." as is confirmed elsewhere in St. Ignatius. Orthodox scholars like Fr. Afanasieff and Fr. Schmemann among several others write that it is no false translation. On St. Ignatius, Father writes, "The Roman Church 'presides' in love, that is, in the concord based on love between all the local churches. The term 'which presides' needs no discussion; used in the masculine it means the bishop, for he, as head of the local church, sits in the 'first place' at the eucharistic assembly, that is, in the central seat. He is truly the president of his church ... the local churches grouped, as it were, in a eucharistic assembly, with every church in its special place, and the church of Rome in the chair, sitting in the 'first place.' So, says Ignatius, the Church of Rome indeed has the priority in the whole company of churches united by concord ... In his period no other church laid claim to the role, which belonged to the Church of Rome. " and on St. Irenaeus, "I think a likelier sense of -convenire- here is 'address oneself to,' 'turn to,' 'have recourse to.' The sense of the remark would then be: every local church should have recourse to the Church of Rome ... This passage in Irenaeus [from Against Heresies 3:4:1] illuminates the meaning of his remarks about the Church of Rome: if there are disputes in a local church, that church should have recourse to the Roman Church, for there is contained the Tradition which is preserved by all the churches." And as we have seen, it is this ancient right of recourse which later synods under Damasus and at Sardica would codify was widely accepted in the East, Constantinople, Jerusalem and elsewhere, St. Maximus, St. Theodore, St. Nicephorus, St. Sophronius and many others bearing witness.
Whose analysis of St. Ignatius are you quoting. You didn't really specify. It's also laughably bad, even if it did come from an Orthodox source. Read the rest of St. Ignatius's epistles.
Read St. Irenaeus in context.
Suppose there arise a dispute relative to some important question among us, should we not have recourse to the most ancient Churches with which the apostles held constant intercourse,and learn from them what is certain and clear in regard to the present question?
Rome was the only Apostolic See in the West, where St. Irenaeus was writing from (Gaul), and since we don't have the Greek original of his work we can only speculate the exact meaning of convenire.