It really depends on who you ask, a Thomist or Molinist. You have presented a Thomist view of predestination quite well, imho, so I will not discuss that. I will then discuss the Molinist view.
A very rough view of Molinism is that God is omniscient and respects the free will of intelligent beings. According to this view, God desires the salvation of all men, and thus He gives what is needed for salvation of all men, no exceptions. However, He also knows which people will reject His graces and gifts beforehand, and yet He still gives it to them. “For God makes His sun rise on the evil and on the good, and sends rain on the just and on the unjust” (Matthews 5:45).
Now let us tackle the first verse you mentioned: “Many are called, but few are chosen” (Matthew 22:14 and other places). This excerpt from an essay explains well how a Molinist would explain it:
I have always wondered about Jesus’ use of the passive voice in describing our prospects for salvation: “Many are called, but few are chosen” (e.g., Matt. 22:14). The parables show a great deal of choosing, of exactly the day-planning and life-determining kind that we now deem central to human existence.
When the king proclaims a feast for the wedding of his son (Matt. 22; Luke 14:16-24), a lot of people choose not to attend because they have already chosen better ways to be the busy deities over their own time; they have already chosen their nap in the lair of the dragon. One man chooses to tend his field, because he has already chosen that good harvests of grain will direct his life. Another man is busy with his merchandise. Another has recently married. Finally, the angry king sends his servants out to find those whose very poverty and debility have sundered them from the illusions of important business: the poor, and the maimed, and the halt, and the blind.
Jesus does not sum up such parables by saying what we might expect, “Many are called, but few are they who choose to attend.” That is certainly because salvation lies in God’s choice and is a gift of his grace alone: “Herein is love, not that we loved God, but that he loved us and sent his Son to be the propitiation for our sins” (1 John 4:10).
But it is also, I think, because some people have chosen **never to be chosen. **
The Lovely Dragon of Choice
And you will see you can use this logic on Romans chapter 9 also.
So that is the Molinist view. Both it and the Thomist views on predestination are valid, you can choose one over the other and it will not affect your salvation.