I think we sometimes (often?) get the relationship between the Biblical narrative and our systematic theology quite badly wrong. I suspect that our forebears were even worse at it than us. We often assume that systematic theology must embody 'timeless truth'; narrative by definition is not timeless. We also often assume that systematic theology takes priority over Biblical narrative; that means that we read the latter through the former more often than not. I think something like this is going on when people say that the Law takes priority over the Gospel - whether they mean that temporally, logically, or evangelistically.
I would argue that close attention to the Biblical storyline indicates that Gospel always comes first.
Let's take as our main exhibit the foundational narrative of the OT, the Exodus from Egypt and the journey to Canaan. It seems pretty clear from the narrative that there is no Law involved in the initial Exodus. The people cry to Yahweh, who hears and rescues. There is no record that they have to do anything to secure their rescue. As they head out of Egypt (and my mind goes to the rather dramatic scene in The Ten Commandments) all they can do is rejoice that God has delivered them. However, it is equally clear that their rescue was not without a purpose. Israel was being delivered from slavery in Egypt in order to serve Yahweh (thus Exodus 3:12, 7:16 etc). So Sinai is the logical destination, the place to go after the Exodus. Once you get there, of course you get the Law - Israel was not being set free in order to wander aimlessly, but in order to receive a new and infinitely better Master.
The point is, structure-wise, it is Gospel, then Law.
That basic structure is repeated throughout Scripture. I think the first example is creation itself, which is certainly presented as a Gospel, and certainly has a Law which follows it. And I am sure it is significant that when you step out of the realm of narrative, into, for example, the Pauline epistles, you so regularly have a structure of Gospel first, followed by instruction. (I will argue at some point that Biblically this instruction is Law - but not in this post). Not only is this clear structurally, but it makes sense of the relationship between Gospel and Law which is described in the OT - but more on this at a later date.
If at this point you're thinking either 'I'm not sure you can make this sort of doctrinal point from the shape of narrative' or 'but in the grand scheme of things, doesn't the Law of Moses come before the Gospel of Christ in the Bible?' - let me just point you to Paul's argument in Romans 4:9-12 and Galatians 3:15-18. Paul makes a great deal of the order of events, and argues explicitly that the Gospel was preached to Abraham centuries before the Law of Moses was promulgated.
The storyline of the Bible is Gospel first, then Law. What impact should that have on our doctrine?