Did Martin Luther believe the Church needed to be reformed before the Great Schism of 1054AD, or after?

First off, no: "Roman Catholicism and Eastern Orthodoxy are basically the same doctrinally" is incorrect. That is beyond the scope of this question, but it's a flawed premise. (See details at the link for an introduction, the issue is somewhat complex).

Did Luther believe that the Church needed to be doctrinally reformed even before the Great Schism?

That's a counterfactual. Having identified the core problem as the Papacy, and noting how long the Papacy had been an influence upon (or in his view, an infection of) the Church, wasn't a matter of "should have" but instead represented something what he could try to fix/reform.
Root cause -> remedy. (Martin Luther was German: think practical!)
That is what he intended to do, and it is important to remember that he wasn't alone as an actor in the Reformation. Outside of the religious context, there was a non-trivial political element to the Reformation involving Emperors, Kings, Princes, and Popes. But in those days, religious and political arenas of action were inextricably intertwined.

Recent studies of the Reformation more often emphasize its social dimension, going beyond the doctrinal issues that divided Europeans. Because religion helped shape every aspect of European life, the practices of the new churches caused major changes. Sacramental ceremonies from baptism to last rites had long marked key moments in the lives and families and communities. By abolishing or changing the sacraments, Protestantism challenged the social meaning of these rituals. The Protestant attack on clerical celibacy emptied monasteries and nunneries and led to a married clergy. This shattered older understandings about sexuality and personal holiness and led to intensified debate about the role of women in society. New ideas about piety caused the abolition of many public festivals in Protestant regions, often against popular resistance. Poor relief and charity meant something different when they no longer served as rich people's way to perform penance.

In politics the fact that the church had been a political as well as spiritual power led to realignments at every level from villages to international diplomacy. Religious adherence became an important factor in political alliances until the end of the Thirty Years' War in 1648.

Beyond that, the Pope had become, at around the time Papal states were established in the 700's, in Italy, equivalent to princes or kings in Europe, as did a lot of high ranking clergy by the time of Martin Luther.

If not then why didn't he just embrace Eastern Orthodoxy, and in turn direct his "reforming" constituents toward the East?

The simple answer for why Martin Luther didn't pursue communion and assistance with the Greek Church is that Martin Luther was part of the Roman Church. He (and others) wanted to fix/reform it. The Greek (Eastern) Church and the Roman (Western) Church had pronounced anathema on each other and had not been in communion (in the most profound sense) for about four centuries. A Church and a religious community might listen to those asking for improvement from within: they weren't going to listen if the reformers were going to import those already anathema. That's adding to the problem, not adding to the solution.

It is doubtful that your proposed course of action ever crossed his mind.

Try to look at this from the context of 1517: Martin Luther was a clergyman who loved his church and wished to wash from his Church -- the body of Christ -- the stain of sin that (as he saw it) was spreading continually by reason of the Pope/Papacy. (Analogy: you don't fix your marriage by getting a mistress, you fix it by working from within to heal the wounds done within the marriage). He didn't want to leave the Church: fleeing to a Church that was anathema (not in communion) would not make sense in his context.

On a practical level, the Greek Orthodox World was under the Turkish thumb (the rule of the Caliphate) and were more or less Dhimi.
By 1454, the Turks had conquered most of the Balkans (Kosovo stands out as a point in history, and the disaster at Nicopolis) and had finally taken Constantinople. When Luther finally nailed the 95 theses to the door of the Wittenberg Castle church in 1517, looking East was looking to the land of the Infidel, the Muslim. There was no help from there. They (any Christians in that part of the world) had problems of their own.

The external enemy of the Church? The Turk. (Still true in 1571 when the Battle of Lepanto was won).
The internal enemy? The Pope. That's the enemy Martin Luther could do something about, someone who was within reach on both the doctrinal and political level.

Luther saw the church becoming significantly corrupted much earlier than we might think. Generally I would say that Luther perceived a split between the 'real' church and the 'false church' basically around the time of St. Augustine, for he always separated the ritualistic ecclesiastical doctrine of religion, from the Augustinian spiritual doctrine of saving grace. To garner direct quotes from Luther in establishing a factual date of the church apostasy, we would do well to start at St. Gregory and the establishment of the papacy, according to Luther, right after at around 603 AD.

While having some respect for Pope Gregory, primarily in that he refused to become a pope in the modern sense of the word, Luther heaps more blame upon St. Gregory (540-604 AD) than anyone before him. In some ways he begins to be a point for galvanizing all the heresies and abominations slowly and gradually building up to that time, making a good first landmark to answer the question.

Gregory alone is the originator of the fables about purgatory. He also originated the Masses for the dead. Somewhere he tells that there was a certain steward in his monastery who by chance and negligence left three guldens among his papers. When Gregory found these after the man’s death, he had made a terrific uproar about the deceased man and had cried out that the man was accursed because of the crime of thievery and would be subject to eternal punishments, although it was likely that this monk had had greater opportunity to steal in other respects; yet nothing had been pilfered by him, but this money had lain hidden among his papers without his knowledge. Yet Gregory declares that by this example and as a result of his shouting the others were so terrified that from then on no one of them was willing to keep back even a heller. Finally, however, Gregory ordered 30 Masses to be said for the man, and when these had been completed—so he writes—this steward appeared to him and thanked him profusely for the great service by which he had been freed from punishments and the curse of God.

This was undoubtedly the “strong delusion” referred to in 2 Thess. 2:11, and from this example of Gregory there spread into the whole world that infinite multitude of abominations and the offering of the sacrament for the dead. But the specter which appeared to him was the devil in all his wickedness, who came out of hell to mock the whole human race. For the horrible and rash falsehood of purgatory and Masses for the dead exceeds all understanding and power of speech. (Luther's Works Vol 7.297)

Another landmark the more direct to the answer would be just after, in Pope Boniface III who Luther technically thought was the first Pope (603 AD) (Unlike the Catholic church of course who assumes the Papacy started way back with Peter).

It is very easy to prove that the pope is neither the commander or head of Christendom, nor lord of the world above emperor, councils, and everything, as he lies, blasphemes, curses, and raves in his decretals, to which the hellish Satan drives him. He himself knows full well—and it is as clear as the dear sun from all the decrees of the ancient councils, from all the histories, from the writings of the holy fathers, Jerome, Augustine, and Cyprian, and from all of Christendom before the first pope, who was called Boniface III* —that the bishop of Rome was nothing more than a bishop and should still be that. St. Jerome dared to say freely, “All bishops are equal, all together they have inherited the throne of the apostles,” and adds the example, “as the bishop of a small city—like Engubium67 and Rome, Regium and Constantinople, Thebes and Alexandria. (Luther's Works Vol 41.290)

On the topic of the papacy Luther does not speak negatively about Gregory at all, rather he seems to admire him in spite of his other low opinions.

In addition, St. Gregory, when it [the title “universal pope”] was offered to him by several great bishops, sharply refused it and writes that none of his predecessors had been so bold as to accept or wish to carry such a title,71 although the sixth council in Chalcedon72 had offered it to them; he closes by saying briefly and to the point that no one should call himself the highest bishop or head of the whole of Christendom, as many decrees also say, and furthermore, that the bishop of Rome too, though he is one of the greater ones, is nonetheless not to be called universalis, the head of “all” Christendom. (Luther's Works Vol 41.291)

It is after Gregory that Luther truly pins the fall of the church under the papacy:

But after Gregory’s death Sabinianus was a bishop for a year and a half; I count him among the popes, for he was a big monster, like a pope is, and wanted to burn the books of St. Gregory, his immediate predecessor—perhaps because in his writings St. Gregory did not want the papacy to be tolerated. Boniface III was elected after him. This is when God’s wrath began. This Boniface persuaded the regicide Phocas that he should be pope, or chief of all the bishops in the whole world. The bell was cast then, and the Roman horror accepted with joy, as the one who was now lord over all the bishops in the world. (Luther's Works Vol 41.291)

One could trace some of the other streams of perceived corruptions by investigating the origins of many practices Luther opposed but I think starting with St Gregory but absolutely occurring with Pope Boniface III (603 AD) followed by the Popes after him is really where the true church under the Augustinian faith split from the ritualistic ecclesiastical church under the corrupt doctrines of the papacy, according to Luther.