In the NT, there is a "new dimension or orientation that has been given to OT ideas and symbols"
Many have a hang up trying to understand the New Testament through the lens of redemptive history because they expect any reference to Old Testament figures and types (including the fulfillment of OT figures in the person of Christ and His church) to have an obvious one-to-one correlation between the OT figure or type and the fulfillment. But the OT is rarely interpreted this way by Christ and the NT authors. The shadows are precisely that: shadows. One is not looking for NT fulfillment to the exact detail of the OT shadow (because the OT shadow was prophetically speaking to its own generation in its own circumstance, while at the same time pointing forward to Christ).
I would leave off with Brown on his very last point, probably (given he's not here to explain it precisely). With Vos and G. K. Beale (who develops this redemptive historical hermeneutic more fully in his essay in "Right Doctrine from the Wrong Texts?", which we have quoted extensively on this blog), I would say Christ is not "reinterpreting" the OT. The Messianic consciousness of the OT authors means the underlying Messianic intent of what they were writing and prophesying was there from the beginning. Christ merely understands that he is THE fulfillment of the inspired revelation coming from their mouths and pens.
And I would add that not only does this new dimension or orientation apply to OT ideas and symbols, it also applies to OT history itself. All of the narrative in the Old Testament prophetically points to Christ. The history isn't recorded for history sake. There is an eschatological trajectory pushing the original audience to see something of a coming "Messiah" in the fulfillment of the promise made in Genesis 3:15, even in the stories and "Bible heroes" that carry along the story of the Patriarchs and Israel through the Old Testament.
Coming to an understanding that the NT fulfillment and the NT's use of the OT does not have to have a one-to-one correlation in every respect changed forever the way I read, study, and preach Christ and Him crucified in the New Testament. It is as Christ told the two on the road to Emmaus and his disciples in Luke 24: "ALL of the Scriptures are about me."