I don't see the pivot, it seems the disciples were already familiar with Jesus' teaching in parables (they asked about it) and Jesus has been announcing the Kingdom since the very start of His ministry (cf. Mt 4). What's the pivot?
The pivot is that he and his disciples had been preaching the message "the kingdom of heaven was at hand and the promised King is among them" (they crucified him for this claim) and calling for a national repentance. In chapter 12 the natinal leaders denied him and convinced the people that he was doing the miracles by the power of Beelzebub, the lord of the flies, thus committing the unpardonable sin. At the last of the chapter, after indicting them for their actions, he announced a new and personal relationship of those who would do the will of the Father and of course, that was to believe on him. In Matt 13, he fulfills the prophecy of Isaiah that he would blind their eyes by speaking to them in parables. This would require those who would be taught of God (he is God) to come to him for understanding. Example: Mt 13:36 Then Jesus sent the multitude away, and went into the house: and his disciples came unto him, saying, Declare unto us the parable of the tares of the field. Mt 15:15 Then answered Peter and said unto him, Declare unto us this parable. The parables must be explained by a member of diety which requires a personal relationship with God and religious people cannot understand them without it no matter how sincere they are. Those who rejected the plain words of Jesus Christ were the most religious of Israel and they did not stop being religious when they rejected him and they continue to this day to say they are the chosen of God. They have synagogues all over the world where they worship him. See 1 Cor 2 to get the explanation of how the thoughts of God becomes the thoughts of man.
There doesn't seem to be a comment beyond two observations, one that some parables span a lot of time, and the other that one of the parables is interpreted personally. I'd conclude they don't all span this amount of time if some are interpreted personally.
In the first parable, the seed that is sown by the sower produces the prople of God and then in the second parable they are sown in the field (the world). 37 He answered and said unto them, He that soweth the good seed is the Son of man;
38 The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one;
39 The enemy that sowed them is the devil; the harvest is the end of the world; and the reapers are the angels.
Mr 16:15 And he said unto them, Go ye into all the world, and preach the gospel to every creature. This is a sowing!
But there is confusion in the world:
2Co 11:14 And no marvel; for Satan himself is transformed into an angel of light. 15 Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works.
These parables in Matt 13 describe this present evil age (Ga 1:4) with the kingdom of God being in the world while the King is not present but being governed by heavenly principles and laws while existing among and beside the kingdom of Satan. That this kingdom is a long period of time is shown by the agriculural analogy of sowing and reaping which takes time to accomplish.
These parables are wonderful but not everyone understands them and I comment on them only because the argument was attempting to make them address a subject outside their intent and context. I hope you can appreciate that.