The Yalkut (40:31) takes the latter approach, and says that the pesukim allude to the following dialogue between Hashem and Iyov.
I'll try to translate.
"Will you finish the Sukkah with the Leviathan's hide?" Rabbah bar bar Channa said: in the future, Hashem will make Sukkos for the Tzadikim. Rav Levi said, whoever fulfills the mitzva of Sukka in this world, Hashem will settle him in a Sukka made of the hide of the Leviathan in the coming future, as it says "Will you finish the Sukkah with the Leviathan's hide."
You find that when suffering came upon Iyov, he complained about his strict punishment and said "If only I could know, if only I could find Him, I would like to know what words He could use to explain what is happening to me!" Hashem answered, "You say you want to know? Look: I will one day make a Sukka from the hide of the Leviathan; if it will be missing one side, will you complete it? If you say 'with the skin of the Leviathan,' is that not praiseworthy?
Rav Pinchas... and Rav Yirmiah... say, the corners of his sides dim the orbit of the Sun... there is no more foul part of a fish than its bottom; the bottom of the Levyasan is as beautiful as gold."
(end of Yalkut)
I can't tell you what this mysterious Yalkut means. But I do know the following:
1. It has something to do with Sukkos.
2. Hashem comforted the tragedy-beset Iyov by showing a connection between the suffering of the righteous in this world and the fact that a Sukka is kosher even when missing one entire wall.
3. It says that only Hashem can complete the fourth side of a sukka made from the hide of the Leviathan.
This may be one of the many medrashim that is so hopelessly obscure as to remain hefker to whatever pshat people want to impute to it. But I am hoping to get a clear and convincing pshat before yomtov is over. I know that Reb Aharon Soloveichik has a pshat in the Yalkut. I have to think about it before posting it.
Chaim B of DivreiChaim.blogspot.com referred me to Reb Tzadok, who says (see comments; it's on page 244 of the hebrewbooks.org volume I) that the idea of Sukkas Oro Shel Liviyasan means that tzadikim, having overcome the Yetzer Hara in this world, will be seated in a sukka made from an animal that represents untrammeled physicality and driving desire, (the Liviyasan being a combination of the Nachash and Dagim, which profligately engage in pirya verivya,) and that this animal was the source of Adam and Chava's "kosnos ohr." Thank you, Chaim. But Reb Tzadok's pshat does not address the connection to Iyov.
See further in the comments for a pshat from the Yismach Moshe that does specifically talk about this Medrash. I'm still hoping for more kipshuto.
Thanks to the wonders of the internet, I received a pshat from the author of the earlier post (on Meva'eit), who said the following:
Sukka is known to represent Hashem's protection and Hashgacha (e.g. Erchin 32b ואגין זכותא עלייהו כי סוכה, and the interchange of Shomer Amo Yisrael Laad <-> Hapores Sukkat Shalom).
Sukka tells us that it is just so that one could be in a place where the 4th wall is missing, the 3rd is only tephach, and the other two are some combination of God, Lavud & Dophen Akumma. Yet, it is a kosher Sukka.
(Note: The writer is referring to the halacha that a sukka does not need four walls. A Sukka is halachically adequate if it has two 'whole' walls, a third wall that is a few inches long, and no fourth wall at all. Even the two 'whole' walls don't have to be whole: they can be perforated and short and afford no privacy or protection.)
We often look around and see holes in this protection shield. Iyyov feels he was left out there, no Mechitzos, no protection around. But, when he would see the full picture, the full Sukka, it should become clear that what looked like nothing around was in fact part of the bigger Sukkat Livyatan. Would he then dare to "fix" it?
And now I understand what I had heard in the name of Reb Aharon Soloveichik. I was missing some minor elements of what Reb Aharon said, but having seen this pshat, it is clear to me that this is precisely what Reb Aharon meant.
The Sukka represents Hashem's protection, the Hashgacha Pratis of Klal Yisrael. But the Sukka, ironically, is the merest scrap of a house-- not only is the roof barely functional, but the walls are merely ideas or symbols of walls, more absent than present. The mussar haskeil is that davka this Sukka teaches us that Hashem's inexorable hashgacha, the hashgacha that makes us indestructible, seems to be so fragile, it's barely there, but is no less real for that. As Reb Aharon said, the Mechitza that is there ahl pi din (tzuras hapesach, pi tikra, omeid meruba ahl haparutz, lavud, dofen akuma, Gud Asik, Pasei Bira'os, and all the dinim we use to create mechitzos, as Reb Eli mentioned) can be more real than a physical mechitza. Similarly, the deficiencies and deprivations we perceive in our life experience are often only epiphenomena; the deeper reality of the richness of a Torah life is truer than that which our limited perception can comprehend.
Yasher Kochachem to Rabbanim and Doctoirim Gary S, Chaim B, and Eli E!
I later saw that the Aruch Laner mentions this medrash too:
Aruch Laner explains that by showing Iyov the halacha that a sukkah is composed of only three walls, of which the third may be only a tefach, Hashem demonstrated that this world's existence is temporary, as it serves as a portal of passage to the eternal world of the souls in the World-to-Come. If a person 's lot is one of suffering, he need not feel that he has been deprived of his deserved comfort and tranquility. In fact, this state of difficulty should provide hope that his true reward will be eternal.