The idea that the Apostles started rethinking, and if fact, contemplated Jesus’ teaching deeply is not at all something foreign to Drefyus’s writing, in fact, he devotes much time to explaining how this factors in to John’s developed Christology. Jesus, the master teacher, understood most clearly of all the doctrine that He was teaching, and the apostles, by contrast, often had to be corrected or have things explained to them. The apostles are even portrayed as stupid by the gospels. The full implications of Jesus’ teaching did not occur to them immediately. In fact, the gospels are quite clear that it was only in the Resurrection that they truly began to understand Jesus’ Messianic role (which they understood perhaps according to the wordly, political messiah paradigm, i.e., reference Christ’s rebuke of Peter).
The problem with your explanation is that it still doesn’t explain the origin of these beliefs. There’s a difference between differing interpretations of varying Jewish schools (i.e., the Pharisees who were indeed the strict observers who interpreted the Law to mean that one couldn’t heal or pick a head of wheat to eat [Jesus Himself refutes this amply, I think]), and something which totally breaks the paradigm of different Jewish schools.
Besides, you unintentionally give the game away-- Jesus calls Himself the Lord of the Sabbath, and in the well-known Temple episode gives Himself authority over the Temple. As more explanation, the money changers in the Temple were necessary because sacrifices could not be bought with unclean Roman money, instead one had to exchange for, ‘pure’ Hebrew money (i.e., shekels). By turning over the tables Jesus was stopping sacrifice in the Temple, because as long as no one had pure money, no one could buy any sacrifices-- he was acting out an eschatological sign for when the Temple itself would no longer have sacrifices!
Perhaps they were willing to listen to Jesus, but these very claims Jesus made could only, ultimately, have been made by YHWH Himself. Who else has authority to interpret the law as such? i.e, It is written… but I say to you… (in the Sermon) Who else has such sovereign authority over the Temple and the Sabbath? The simple fact is that Jesus both taught and acted as if He was YHWH Himself. Pay closer attention to the gospels next time and observe how He must hint at His divinity in this Jewish context… one greater than Solomon is here, one greater than Moses is here, one greater than Abraham is here. There is no one greater than Moses in Jewish thought, save YHWH Himself.
Jesus at every turn, as N.T. Wright would say, is subversive of traditional Jewish symbols-- the land (give away your possessions! remember, Jews and their connection to the land of Israel), family (hate your mother and father? let the dead bury their dead?), Temple/Priesthood, and in turn gives new symbols-- supplanting the Temple with the universally attested ritual, the Last Supper, the, “new covenant in His blood” (again, a clear reference back to when Moses inaugurated the first covenant).
All of this, which the disciples did, albiet, without understanding fully, follow Him in. If you take it as evidence of them defecting from the Jewish faith, as you did with the Sabbath, it is only evidence that Jesus taught things which only YHWH Himself could teach-- in other words, that Jesus taught these doctrines concerning His divinity.
I think you still need to try to explain, plausibly, how these Jews could take on what would apparently be such idolatrous and blasphemous positions, if it were not that Jesus taught them. And also, that they weren’t also confirmed-- if Jesus taught them, and was crucified (and they clearly did not understand the idea of the Suffering Servant adequately during His life), then He was a failed Messiah and His teaching was bankrupt. A successful Messiah was excepted to be a political conqueror, and that perhaps would have been enough, but Jesus was not this type of Messiah and He was also crucified. We need both Jesus to teach this doctrine, and for God to confirm it. Let’s not forget, we’re talking about first century, Second Temple period Jews. Religious tolerance, and such, the idea that all religions are equal, etc., these aren’t exactly the mode of operation for Jews of the time. They had to have some reason why they could overcome these objections. As Dreyfus said, “if we are to surmount these obstacles, we certainly need a number of extremely strong reasons which will produce crystal clear certitude.” I want to emphasize, especially for Jews, they would have needed a tremendous reason not to abide by the reasoning which he included in, “b. the Jewish milieu.”