Great perspective! I agree that diving into the Bible to find the Jewish roots of Christianity is very important. Besides the Old Testament, the New Testament has also been almost exclusively written by Jews (at least in an ethnic sense). Probing as to what the biblical basis is for the fulfillment of the old covenant -and then discerning what that actually means- seems crucial to constructively pointing to the Hebraic heritage we share.
Would you also see a place for contemporary considerations such as the return of the Jewish people to the promised land?