There should be no real problem for the Assyrians to reunify as there is no real dogmatic difference involved here.
Reunion involves more than the wish for organizational, sacramental or faith-based agreements. It has more to do with a sense of compunction on the sides seeking reunion in the first instance. Historically, it involved the repentance of those individuals or churches that were excommunicated. Today, the tendency in ecumenical talks is to see everyone as having sinned for being in a state of mutual excommunication.
That is fine as far as it goes but it should not gloss over the real doctrinal differences that gave rise to the separation in the first place.
At the same time, both sides or all sides should be willing to come to a better understanding of each other's positions to determine if, in fact, the heresies condemned are really the positions maintained by the others.
The situation with the Assyrians dates way back to the time of Emperor Justinian who wished to come to a religious settlement with the Miaphysites or Oriental Churches for the sake of unity of the empire.
An amateur theologian, Justinian dabbled in religious affairs where he had no business being. He was easily swayed by those, like the Origenists, who wanted to prevent the condemnation of positions said to have been espoused by Origen and of Origen himself, so they tried to persuade Justinian to focus on the Antiochene school of Christology and the teachings of Diodore of Tarsus and Theodore the Interpreter, both of whom continue to be highly venerated as the Greek Doctors, along with Nestorius who was actually the smallest actor in the Nestorian struggle. And this Justinian did. Theodore of Mopsuestia died in the peace of the Church as did Diodore. Both were well known to St John Chrysostom who studied with Theodore.
St Cyril of Alexandria, well before his diatribe against the Antiochene School, said that "As Theodore believes, so does the Church believe." Pope Vigilius refused to condemn Theodore and was found in contempt of the imperial Byzantine court and we know the rest of the story. Nestorius was a friend of St Flavian who was beaten to death at a council by Miaphysites. Pope St Leo I was long considered a "Nestorian" by the Oriental churches because he was a "Dyophysite" or someone who affirmed two Natures in Christ. The Miaphysites affirmed only "One Divine-Human Nature" in Christ or "One Divine Nature of God the Word Incarnate" using St Cyril's words.
When Orthodox theologians in talks with the Oriental theologians pressed the matter, it came out that "Physis" or "Nature" for them meant the same as "Person" does for the Orthodox.
That is why, to the consternation of Orthodox theologians, the Miaphysites could, in the same breath, speak of "One Divine Nature of God the Word Incarnate" and then affirm that Christ's Divinity and Humanity were distinct etc.
Yes, the Apostolic Churches ought to be united. And yes, the social sciences should be brought to bear on historic theological issues to determine just WHAT theologians and teachers of old meant with their terminology and the relation between church and state.