Your raise a lot of interesting points that are sources of great controversy between different Christian groups, but I'll try to focus on your question:
What is an overview of the theological differences that led to
distinct approaches to unwanted State innovation and overreach in the
West and East?
I don't think there really was much distinction between West and East along what the author suggests during the first millennium.
Ambrose did, indeed, excommunicate Theodosius I (for a massacre he ordered in Thessalonica), but his excommunication was not indefinite and, according to the Greek Synaxarion, lasted eight months. His excommunication by Ambrose took place outside the cathedral church of Milan and was quite public (The Lives of the Saints of the Orthodox Church, vol. 2, Holy Monastery of Simonos Petra, Mt. Athos, 1999, p. 343). The Emperor's response was to fall to Ambrose's feet weeping. "Theodosius returned to his palace troubled and sorry for his transgression," writes Dmitri of Rostov. "He submitted to the sentence the saint laid upon him, doing public penance with commoners. He was not ashamed to lie prostrate in the presence of his subjects" (Great Collection of the Lives of the Saints, December, John Chrysostom Press, 2000, pp. 160-161).
In order to demonstrate that the West and East had "distinct approaches", one must look at cases of how the Western and Eastern Patriarchs behaved in very similar circumstances. The circumstances surrounding the disputes between Germanus and Leo on one hand, and Theodosius and Ambrose on the other, could not be have been more different. Whereas Theodosius was a generally pious emperor who bore reproaches from the Church with humility and lived a life of repentance, Leo was nearly the opposite. After announcing that he was going to remove all icons from public worship - on his own initiative - he subsequently beat Germanus, sent his troops to burn down the Patriarchal School in Constantinople, and then set him in the midst of a large assembly of senators and dignitaries to force him to accept his decree to destroy all icons in the empire.
Secular and some Protestant historians frequently attribute the actions of Church hierarchs to some self-serving, political goal, in the tradition of Edward Gibbon - not considering at all the possibility that actions may have actually been undertaken for the spiritual benefit of those concerned. There is nothing at all in any of the accounts we have that Ambrose was some sort of political manipulator, trying method after method to control emperors until he finally "hit on one".
In reading Dr. Shelley's book (I bought myself a copy), I was stunned to find that he devotes no coverage at all to , nor even seems to be aware of, what was probably the single most important event in Christian history following the first millennium; namely, the Great Schism that occurred between the See of Rome and the other four ancient Sees of the Church. The See of Rome formed what is known today as the Roman Catholic Church, while the remaining Sees today comprise the Eastern Orthodox Church. I would suggest that anyone reading this who desires a more accurate and comprehensive view of Church History in the first millennium to consult Kallistos Ware's The Orthodox Church, available from Penguin Books. Following the Schism, a great difference in character between East and West did, in fact, emerge as you suggest. Met. Kallistos explains how this developed as follows:
East and west were becoming strangers to one another, and this was
something from which both were likely to suffer. In the early Church
there had been unity in the faith, but a diversity of theological
schools. From the start Greeks and Latins had each approached the
Christian Mystery in their own way. At the risk of some
oversimplification, it can be said that the Latin approach was more
practical, the Greek more speculative; Latin thought was influenced by
juridical ideas, by the concepts of Roman law, while the Greeks
understood theology in the context of worship and in the light of the
Holy Liturgy. When thinking about the Trinity, Latins started with the
unity of the Godhead, Greeks with the threeness of the persons; when
reflecting on the Crucifixion, Latins thought primarily of Christ the
Victim, Greeks of Christ the Victor; Latins talked more of redemption,
Greeks of deification; and so on. Like the schools of Antioch and
Alexandria within the east, these two distinctive approaches were not
in themselves contradictory; each served to supplement the other, and
each had its place in the fullness of Catholic tradition. But now that
the two sides were becoming strangers to one another – with no
political and little cultural unity, with no common language – there
was a danger that each side would follow its own approach in isolation
and push it to extremes, forgetting the value in the other point of
We have already had occasion to mention the Papacy when
speaking of the different political situations in east and west; and
we have seen how the centralized and monarchical structure of the
western Church was reinforced by the barbarian invasions. Now so long
as the Pope claimed an absolute power only in the west, Byzantium
raised no objections. The Byzantines did not mind if the western
Church was centralized, so long as the Papacy did not interfere in the
east. The Pope, however, believed his immediate power of jurisdiction
to extend to the east as well as to the west; and as soon as he tried
to enforce this claim within the eastern Patriarchates, trouble was
bound to arise. The Greeks assigned to the Pope a primacy of honour,
but not the universal supremacy which he regarded as his due. The Pope
viewed infallibility as his own prerogative; the Greeks held that in
matters of the faith the final decision rested not with the Pope
alone, but with a Council representing all the bishops of the Church.
Here we have two different conceptions of the visible organization of
Pope Innocent III belonged to the post-schism era. In addition to whatever abuses may have been committed by him, he is also credited with the sack of Christian Constantinople during the Crusades in 1204. Pope John Paul II apologized for the event to the Patriarch of Constantinople 800 years later.