As I read through a load of books for my comprehensive exams I have found three different justifications for reading the Bible figurally. The first and least dealt with in the last two or three hundred years is the ontological approach, which, in believing that all effects bear the mark of their cause, teaches that all created things bear the mark of their Creator. Origen, Augustine, and Maximus are the classic examples of this kind of reading, Aquinas and Wyclif are good Medieval exponents, and the Hutchensonians, the early Tractarians, and my man Lionel Thornton are good modern exemplars.
Second, there is the more modern turn to the Biblical author who intentionally fashions a figure in accordance with the conventions of a particular genre. Charles Gore is a good example for this category, and indeed most orthodox Anglicans in the twentieth century held some version of his views on authorial intended figures.
Finally there is Gabriel Hebert's liturgical justification for figuration. For, we read the Psalms in the community, and if we assume they have relevance for us, then we are going to have to spiritually apply them to ourselves. And not just us, but Jesus himself did this in the synagogue. This might be a more specific example of another explanatory framework for the Gospel's figuralism, namely, that Jesus and the Apostles just reinterpreted and reapplied images that were floating about in Israel (both Austin Farrar and N.T. Wright are good examples of this approach). I'm not much into this latter more general "reinterpretation" view. It seems a little embarrassed with bluntly proclaiming that Jesus fulfilled the OT. Still, the more specific liturgical application of the Psalms to new settings does seem to have something to it. (Perhaps this liturgical approach is just a sub-category of the previous genre approach. I don't claim that these are hard and fast divisions; they all hold to some degree or another.)
It is a bit tangential, but I wanted to get to another point in order to ask a Christological question. There has been a on-going debate among theologians about whether the whole of the Psalter prophetically applies to Jesus or not. Because Jesus was not a sinner, it is alleged that those Psalms that speak of the Psalmist's sin and repentance could not have applied to him. One could take an ontological approach (as I like to) and observe that Biblical words are God's words--the Psalms of repentance included, and Jesus is God, so the Psalms of repentance are Jesus' words of repentance (traditionally understood in a vicarious way). The other approach is simply to ask whether Jesus would have recited these Psalms in the synagogue. Is it realistic to think that when everyone else was reciting Psalm 51 that he would be silent? Or that he would speak some of the sentences and then abruptly stop at others within the same Psalm? I think this is silly. If he did recite them, then we obviously need a doctrine of accommodation to say in what way he could have truthfully said them. But this is to do rather traditional figural exegesis.