According to the opinions that Iyov did not live in the days of Moshe, who wrote his Sefer?

Question

Bava Basra 15a-b lists a number of opinions as to when Iyov lived:

• R' Levi bar Chama: In the days of Moshe
• Rava: In the days of the Meraglim
• Unnamed student of R' Shmuel bar Nachmani: Iyov never lived; it's entirely a mashal
• R' Yochanan and Rav Elazar: Beginning of Bayis Sheini
• Simple understanding of an unattributed Braisa: During Galus Mitzraim
• R' Eliezer: In the days of Sefer Rus
• R' Yehoshua ben Karchah: In the days of Achashveirosh
• R' Nassan: In the days of the kingdom of Sheva
• Chachamim: In the days of the Kasdim (i.e. Nevuchadnetzar - Rashi)
• Yeish Omrim: In the days of Yaakov

The Gemara ibid. quotes a Braisa that Sefer Iyov was written by Moshe Rabbeinu; this opinion can only hold according to R' Levi bar Chama, Rava, the student of R' Shmuel bar Nachmani, the unattributed Braisa, and Yeish Omrim. According to the remaining six opinions, Iyov lived after Moshe.

According to these opinions, who wrote Sefer Iyov?

Answer 1

To clarify a little, Rabbi Eliezer thinks it was in the time of the Judges, not necessarily in the time of Ruth. It's true that he uses a phrase from Ruth ("בימי שפוט השופטים"), but he doesn't state that it was necessarily in her time.¹

Rabbi Ahron Marcus in Barzilai, pg. 252, brings the view of Rabbi David of Lelov that it was written by Yehonatan ben Gershom ben Moshe (Menashe in the ketiv, with a hanging Nun), after he did teshuvah for becoming Dan's priest in the story of the idol of Micha (Shoftim 18). This view was based on a tradition that the rabbi had. Rabbi Marcus then sets out to prove this view.

Rabbi Ze'ev Yaavetz in Toldot Yisrael, vol. 3, pg. 90, agreed with the view that he lived in the time of Galut Bavel and thought that he himself was the person who authored the book. According to Rabbi Yaavetz, he was a wise and famous man in the time of the Galut.

Da'at Mikra in their introduction to the book, pg. 18-19, suggest that Iyov himself was probably a man who lived in ancient times, perhaps even around the time of Noach, but the author of the book was likely someone from Yechezkel's generation.

In this post on the Otzar Hachomah forum, the commenter brings a view that though written in an archaic style, seems to be his own, and suggests that if the story took place in the time of the judges or the time of Sheva, then it most likely became known to Am Yisrael only after the time of Daniel, therefore, it is most likely that Anshei Knesset Hegedolah wrote it (being that they also authored Daniel).

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¹ In fact, even the phrase from Ruth is ambiguous.