Those who insist that God's choice is determined in some way by man (man's faith, man's action) place the "mystery" of salvation in the wrong place:
Hope, faith, and love are (first) infused when a man receives the sacrament of baptism. Man is not able to have the (supernatural) faith and do God pleasing deeds, without sanctifying grace. So I agree, God doesn't predestine based on these. But, what about man's freely willed decision to cooperate with grace? What about the
voto mentioned by the Council of Trent. God foreknows the will, the
voto.
There is no merit involved, since all merit comes from the blood of Christ, and is
communicated (Trent) to the candidates.
I can't understand, why predestination should be that mysterious. God has revealed who will be saved:
We know that to them that love God, all things work together unto good (Rom 8:28)
For whom he foreknew, he also predestinated to be made conformable to the image of his Son (Rom 8:29)
he who endures to the end will be saved (Matt 24:13)
St. Thomas Aquinas avoids to consider the role of the of the free will, although he mentions it without further consideration:
This call is necessary, because our heart would not turn itself to God, unless God himself drew us to him: no one can come to me unless the Father who sent me draws him (John 6:44); turn us to thyself, O Lord, that we may be turned (Lam 5:21). Furthermore, this call is efficacious in the predestined, because they assent to the call: everyone who has heard and learned from the Father comes to me (John 6:45).
https://aquinas.cc/la/en/~Rom.C8.L6.n707Thomas mentions the way in which "God's choice is determined in some way by man" (DecemRationis). God would prefer to predestine all men, since he wills to do so. But he is limited by man, since the predestined have to freely assent to the call (excepting exceptions). God cannot predestine someone who doesn't want to assent (or who later backs down).
I don't understand why St. Thomas doesn't infer that God's foreknowledge of this assent of the predestined is key to solve the "mystery" of predestination.
Your point ...
And the free choice of God of how a man is saved - by being baptized and persevering in the Catholic faith - is no more "unjust" than His free determination of which man to save.
... is not concerned. Since even a less mysterious predestination doesn't invalidate it.