Hi Sherman,
There is no evidence that the quote above was the personal opinion of Shammai himself. The students of the school he established (“Beth Shammai”) were known to have held to theological positions in opposition to the school of Hillel (“Beth Hillel”), which were not necessarily the exact positions of the two rabbis themselves:
jewishvirtuallibrary.org/jso … illel.html
jewishencyclopedia.com/view. … 6&letter=B
The school of Shammai continued a good while after the death of Christ. In the article from Jewish Encyclopedia we read, “Bet Shammai and Bet Hillel continued their disputes—probably interrupted during the war times—after the destruction of the Temple, or until after the reorganization of the Sanhedrin under the presidency of Gamaliel II. (80 C.E.)” So what you quote above could simply have been the most recent known position of the students of Shammai’s school (which was the less popular of the two schools). By the time the statement expressing the position of his school appeared in the Babylonian Talmud (the codification of which took place in the 5th century), this was the known consensus of the students of the school, and not necessarily a direct quote from Shammai himself or even a reflection of his personal opinion while he was alive. So the quote from “Beth Shammai” as it appears in the Babylonian Talmud is actually no evidence that the Pharisees in Christ’s day believed in temporary or remedial punishment.
What is the source of the last quote above? The Babylonian Talmud speaks of people being punished for 12 months, but the implication is that they would be annihilated after that. Akiva ben Joseph is said to have believed that the suffering of the wicked in Gehenna was for only 12 months (books.google.com/books?id=C_d3-K … A9&f=false - see Chapter 2 Mishnah 10) but he lived after Christ’s day (ca.50–ca.135 CE). If this had been believed and taught by a rabbi before him I think it’s likely that the Mishnah would’ve mentioned it. Since it doesn’t, I think we can safely assume that this was not being taught before or while Christ was alive. Also, there is no suggestion that Akiva ben Joseph’s opinion was prevalent among the Jews even in his day.
I think Josephus failed to mention it because it was either a minority view among the Pharisees or it was not known to him. As far as the Mishnah and Talmud, I do think these works carry much weight as evidence of what was being taught by certain rabbis when these works were redacted, but they were redacted after Christ’s day.