My thinking here is driven primarily by what I see is the flow of thought of the section. It seems that chp. 13 is connected intimately with chp. 12, with the central contrast being "love" is greater than/better than/more holistic than the exercise of spiritual gifts within the body. Almost as though love is being held out as the sum total descriptor of true Christian life which must encompass all the other practices for them to have any value. Since the various things introduced--prophecy, tongues, knowledge--all are categories which would fall within the spiritual gifts discussion, I take this to be a sort of restating the case that love is greater, with the addition of the point that love does not fail/cease/pass away.Could you say more about "but if they convey something more like the Christian faith and the Christian hope? This might well be something I am missing, but I don't quite manage to finish the thought here.
As you point out, ἀγάπη stands in parallel with πίστις, ἐλπίς, ἀγάπη, suggesting that the latter form is equally an appropriate way to represent the central essence of Christian life, as Paul sees it. πίστις can have a creedal sense in Paul's writings (which is most evident in the Pastoral Epistles where most of the articular uses are in this sense, as well as a couple non-articular, according to Mounce's Word Biblical Commentary). Speaking of articularity, it is intriguing that these three words are all anarthrous, but I digress. The point is that Paul uses πίστις with a broader range than just "belief in the present time of non face to face with Jesus" sense of the term, so it is not crazy to suggest that πίστις could meaningfully persist into the eschaton. By analogy to trinitarian arguments, ἐλπίς tags along with the first two to form a triad of virtues that sum up the essence of the Christian life in a way that is greater than the spiritual gifts that have been the topic of discussion and which will fade away.Ἡ ἀγάπη οὐδέποτε πίπτει
νυνὶ δὲ μένει πίστις, ἐλπίς, ἀγάπη, τὰ τρία ταῦτα· μείζων δὲ τούτων ἡ ἀγάπη.
I still haven't quite put my finger on how to tie together what I am seeing (or think I am seeing) here. This is largely a reading driven less by the νυνὶ δέ and driven more by the broader context and my perceptions of Pauline theology. I just find it really significant that knowledge, prophecy, tongues, etc. are all put in a framework where they are described in terms of change they will undergo, whereas love (and faith and hope) is contrasted against them in a stative assertion: μένει. They change from this age to the next; love seems to remain the same, thus making the life of love valuable now and forever, whereas any heap of knowledge acquired will eventually be seen as child's play, at best.
I don't know if that makes sense, but it at least raises the significant issue of how this verse fits into the broader context of 1 Corinthians and Pauline theology.