I don't follow your test case. Obviously, a murderer who is regenerated by the Spirit is going to repent. I may know if the Spirit has regenerated him if he repents and believes.
If by double predestination, you mean that God has always known whom He was going to have mercy on based on His grace, and whom He was going to judge based on His justice, then absolutely. That's Romans 9. Why one and not the other? "Not because of him who wills or him who runs but God who has mercy."
If by double predestination you mean equal ultimacy, where God causes the sinner to be evil against his will, then we've always rejected that.
I don't see the Gospel described as an offer, rather, 1 John 3 describes it as a command. A command that we are not able to do, because of our sinfulness, unless the Spirit regenerates us:
No.
Calvin believed: Double predestination as the idea that not only does God choose some to be saved, he also creates some people who will be damned.
Some modern Calvinists respond to the ethical dilemma of double predestination by explaining that God's active predestination is only for the elect. God provides grace to the elect causing salvation, but for the damned God withholds salvific grace.
Calvinists teach that God remains just and fair in creating persons he predestines to damnation because although God unilaterally works in the elect producing regeneration, God does not actively force the damned to sin.
Double predestination may not be the view of any of the Reformed confessions, which speak of God passing over rather than actively reprobating the damned.
However.... Calvin rejected such a position, stating: "This they do ignorantly and childishly since there could be no election without its opposite reprobation ... whom God passes by he reprobates, and that for no other cause but because he is pleased to exclude them from the inheritance which he predestines to his children.
Calvin, Institutes of the Christian Religion
Again, if God created all men in his image, sent his son to die for us through the God Man Christ.... How does this concept make sense except to create further esoteric definitions of who is and isn't saved and who can and can't be part of the club.
Restated: God created some of us specifically to be saved and some specifically to be punished?
That does not align with Christ's sacrifice on the cross.
He created all of us to be saved. Yet many chose, through their rejection of Him and through rejecting the sacraments and living a life in pursuit of salvation, to be castigated from the fires of hell through our own free will. That is different than God prescribing hell for some and heaven for others in a preordained manner.
The sort of thought is what lead to the Anabaptists sex death cult on Germany. Feel free to look up their beliefs and see that they shared many of Calvin's.
This is ultimately the issue with Protestant Theology. There is so much sectarian beliefs built from one person to another that after 300 + years, the approach is a combination of Catholic legalism, and Western individualism to establish what is and is not true Christianity..