THE ANSWER
The main question is based on a misreading of referred passages; all subsequent questions inherit the mistake, and also rely on the false premise, based on one another misreading.
First misreading
Miracoulous gifts, namely, a gift: 1) a word of wisdom, 2) of a word of knowledge, 3) of faith, 4) of gifts of healings, 5) of in-workings of mighty deeds, 6) of prophecy, 7) of discernings of spirits, 8) of kinds of tongues, 9) of interpretation of tongues, -- are all active forces, given to humankind; while prophesies, tongues, and knowledge, for which the questioner asks specifically, are phenomenal occurences, in simple words, they are things.
All spiritual gifts, which Paul recounts, except the first one, are of something, but not as if "gifts made off of somethings", but as "gifts creating such somethings"; including three gifts which the questioner asks specifically, which are gifts "δὲ προφητεία" (of propheteia), "δὲ γένη γλωσσῶν" (of geni glosson), "δὲ λόγος γνώσεως" (of logos gnoseos).
1 Corinthians 12:4-11, YLT:
4 And there are diversities of gifts, and the same Spirit;
5 and there are diversities of ministrations, and the same Lord;
6 and there are diversities of workings, and it is the same God -- who is working the all in all.
7 And to each hath been given the manifestation of the Spirit for profit;
8 for to one through the Spirit hath been given __ a word of wisdom, and to another, of a word of knowledge, according to the same Spirit;
9 and to another, of faith in the same Spirit, and to another, of gifts of healings in the same Spirit;
10 and to another, of in-workings of mighty deeds; and to another, of prophecy; and to another, of discernings of spirits; and to another, of kinds of tongues; and to another, of interpretation of tongues:
11 and all these doth work the one and the same Spirit, dividing to each severally as he intendeth.
Every gift, -- except a word of wisdom, which is a manifestation by itself, while manifestation of word of wisdom would a pure unrestricted act, due to wisdom be covering everything, -- is a manifestation of a thing.
Hence, 2) manifestation of a word of knowledge may come up as a new engine invention, or geologiacal discovery, 3) manifestation of faith may come up as an unmatched physical endurance, or stubborness in doing one particulal thing, 4) manifestation of gifts of healings may come up as massage, surgical, physiological skills, 5) manifestation of in-workings of mighty deeds comes up as anything that is not usual, 6) manifestation of prophecy comes up as foreknowledge, foresight of certain actions and happenings, 7) manifestation of discernings of spirits may come up as understanding intentions of living beings, 8) manifestation of kinds of tongues comes up as understanding minds and reasoning of humans, 9) manifestation of interpretation of tongues comes up as viable explanation of certain text, or certain act, or certain happening, if we widen up a notion of tongue for a little.
In 13:8, Paul speaks about things that happen. He does not speak about gifts that make things.
1 Corinthians 13:8, YLT:
The love doth never fail; and whether δὲ prophecies, they shall become useless; whether __ tongues, they shall cease; whether __ knowledge, it shall become useless;
Even though there is of before prophesies in this verse, it only used here once, and conveys different meaning, which is not "of" but "and", used together with opening sequence of repeated "whether".
Therefore, the title question "Does 1 Cor. 13:8, 13 teach that faith, hope, & love will outlast miraculous gifts?" is based on misreading of 13:8, presuming that Paul speaks about actual spiritual gifts there, while in fact Paul speaks about existential manifested non-personal things, i.e. about wordly human phenomenas. So, the answer is no, because the question is erroneously stated.
Second misreading
Hope and faith are shades of love. Faith looks onto the present, rooting into the past, hope looks into the future, standing onto the present.
1 Corinthians 13:7:
YLT | all things it beareth, all it believeth (pisteuei); all it hopeth (elpidzei), all it endureth.
TR | πάντα στέγει πάντα πιστεύει πάντα ἐλπίζει πάντα ὑπομένει
1 Corinthians 13:13:
YLT | and now there doth remain: faith (pistis), hope (elpis), love -- these three; and the greatest of these is love.
TR | νυνὶ δὲ μένει πίστις, ἐλπίς, ἀγάπη -- τὰ τρία ταῦτα; μείζων δὲ τούτων ἡ ἀγάπη.
Hence, the question "do the gifts of prophecy, tongues, and knowledge end before faith and hope end?" is based on the false premise that 'faith and hope will end', while in fact they will never end, because love will never end, and they are shades of love as it is clearly said in 13:7.
Conclusion
The answer on the central question, "Considering both of these verses, should we conclude that Paul sees faith, hope, and love as outlasting the gifts of prophecy, tongues, and knowledge?", -- is no, we should not conclude that, at least because 13:8 does not speak about spiritual gifts.