Did Jesus set aside divorce (Deu. 24:1) and replace it (Matt. 19:9)?
As partially answered elsewhere (the first link provided by the OP), there is a great distinction between the Old Law and that of Christ's new teaching.
The Mosaic order was reinstituted in another form upon the inauguration of the new priesthood (Heb. 7:11-12), one in which all saints partake as priests (cf. 1 Pet. 2:9). As pointed out in the OP, this is particularly significant based on Jesus' Sermon on the Mount, in which He repeated many of the O/T laws beginning with "You have heard it said..." while replacing them with His new commands (paraphrased):
"You have heard it said":
1. "You shall not commit murder, but he who hates his brother has committed murdered in his heart" (Matt. 5:21-22).
2. "You shall not commit adultery, but he who lusts in his heart has committed adultery..." (Matt. 5:27-28).
3. "He who divorces his wife and marries another commits adultery" (Matt. 5:31-32).
4. "You shall make no false vows... But I say make no oath at all" (Matt. 5:33-37).
5. "An eye for an eye... turn the other cheek" (Matt. 5:38-39).
6. "You shall love your neighbor and hate your enemy... love your enemies, pray for those who persecute you" (Matt. 5:43-44).
We should never feel free to dismiss anything Christ said. Every commandment He spoke is paramount. The 613 laws and ordinances under the Mosaic regime have been superseded by a much stricter set of laws that comprise the Law of Christ (Gal. 6:2). Just as He tells us, and as stated in the OP:
Matthew 19:8-9: "Because of your hardness of heart Moses permitted you to divorce your wives; but from the beginning it has not been this way. 9And I say to you, whoever divorces his wife, except for immorality, and marries another woman commits adultery" (emphasis added).
Are we to accept ALL teaching by the Son of God?
Christ nailed the Law of Moses to the Cross (Col. 2:14), by reaffirming it through His Own commandments (only a few of which are listed above). The new laws are far more comprehensive than anything written in the Old Law.
Let us address the other point stated in the Gospel of Matthew by the OP:
Matthew 5:17-19: “Do not think that I came to abolish the Law [of Moses] or the Prophets; I did not come to abolish but to fulfill. For truly I say to you, until heaven and earth pass away, not the smallest letter or stroke shall pass from the Law [of Moses] until all is accomplished [Christ's death, burial, resurrection]. Whoever then annuls one of the least of these commandments [His new teaching], and teaches others to do the same, shall be called least in the kingdom of heaven; but whoever keeps and teaches them, he shall be called great in the kingdom of heaven" (emphasis added).
Observe 3 points about verse 19 (as well as the bracketed notation):
I. Early in His ministry, Christ says that "not the slightest letter or stoke shall pass from the Law [of Moses] until all is accomplished." What exactly, was to be accomplished? Answer: His Own Sacrifice for humanity? YES, Christ came to "fulfill": it was the Law of Moses He would fulfill. Upon His resurrection, the new Law was instituted, the Law of Moses being nailed to the Cross (Col. 2:14). There is a distinction between fulfilling the Old Law and perfecting it in the New.
Christ took the Law of Moses out of the way. He did so not by violating it but by completing it. This was accomplished through
1. His absolute obedience to it,
2) His fulfillment of His role as the promised Messiah, and by
3) His elevating all the O/T laws to a higher, purer standard: The Law of Christ.
II. Christ tells us that those who violate one of His commandments, has violated them all. His "new commandments" would comprise the Gospel, that was subsequently written after His Resurrection and following Ascension to heaven.
III. Note that in verse 19 (Matthew 5), Christ tells us that anyone who: "[does and teaches]" the commandments of Christ, is he who "shall be called great in the kingdom of heaven."
Observe Coffman's commentary on Matthew 5:19:
In this verse, Christ plainly refers to [His] own commandments with the strong warning that men are under obligations to heed and observe the laws [He] gives. Today, there are some who speak of certain Scriptures as "mere command" But Christ made [His] commandments to be of overwhelming importance and set forth the principle that "the least" of his commandments was to be received and honored with [respect] and obedience. (Emphasis added.)
Christ Law has superseded the Law of Moses — in this case, specifically regarding the new Law on divorce.