Galatians is not the place to go to if you want to get a full-orbed understanding of Paul's view of the Law of Moses. It is, I think, an angular book, with lots of sharp edges. Any attempt to fit it into a systematic framework seems to fail - I have taught through it five or six times now, and every time I think I have it sorted I notice another corner poking out through a tear in my systematic theology. Over time, I've decided I'm okay with it. The purpose of Galatians is not, I think, to teach systematically about the relationship between Law and Gospel, but to burst through all our thinking and disrupt it - just as the Gospel itself bursts through all our human activity and disrupts it.
I think Galatians is primarily about cutting through one particular understanding of the relationship between human and divine activity. The link that the Apostle wants to sever is the one leading from human action to righteousness in the sight of God - where that righteousness is understood to include not only legal justification, but also the right relationship with God and with his covenant community that such justification entails. In Paul's world, the most obvious and most aggressively supported form of this link from human action to righteousness is the Law of Moses. The Gentile Galatians are being urged to accept it. Paul, I think, advances two arguments to explain why Gentile Christians should not adopt the Law of Moses:
1. An argument about the function the Law always served. The issue in Galatia seems to be that the Christians are being tempted to believe that they must pursue the Law of Moses in order to be righteous. This expresses itself in table fellowship - incidentally showing how corporate and communal the concept of righteousness in the NT, against our individualistic understanding. Elsewhere, Paul makes it clear that observance or non-observance of the Law of Moses is irrelevant - he is indifferent as to whether you observe or not. Only you must not make the Law a matter of righteousness, because to do so is to confuse the Law with the Gospel. Righteousness comes by faith in Christ - Christ as promised, for those who lived before his advent; Christ as present for those of us who live after his incarnation. The Law never was meant to bring this righteousness.
2. An eschatological argument. To adopt the Law now is particularly perverse, because the Law of Moses had a time-limited role. It was about keeping Israel looking forward to the Messiah, to bind them closely to the promise. Paul's argument here is complex, and there are parts which I think no-one understands, but the basic point is simple - the role of the Law was to keep the heir looking forward to the inheritance, which is now given in Christ. The Law is therefore passe. It will not do, incidentally, to try to find some part of the Law which is not subject to this argument - either by dividing it into ceremonial, civil, and moral or by any other means. The Law is in the past; Christ is the present and the future.
All well and good, and this seems to suit the Lutheran positioning of the Law very well - the Law comes first and prepares the way for the Gospel. Except for two things. The first is Paul's insistence that the Gospel came first in time. This is clearly very significant for Paul's argument, because it shows that the Gospel was always the point of the Law - the former did not replace the latter, because it came before it and always underpinned it. (One is reminded of John the Baptist - he is before me (in rank) because he was before me (in time) - Paul's argument is formally similar).
The other thing is that when it comes to positive instruction about the shape of the Christian life, Paul is happy to quote the Law of Moses. Is he saying that Christians are, in fact, bound to keep the law of Moses? Absolutely not. But he is pointing to the fact that the Christian life is not one of shapeless freedom. It is one of fulfilling the Law of Christ.
I submit, then - with the reservations that must follow from my first paragraph - that Galatians breaks the link that moves from human activity (according to the Law) to righteousness in order to forge a link that moves from righteousness to human activity (according to the Law, although not that of Moses). And this, I contend, is the pattern of all Scripture.