I’m just going to take one verse you quoted to show where you are in error.
You said “
The result of regeneration is peace with God (Romans 5:1)”
That isn’t what the verse says. So why pretend that it does?
If you read Romans chapters 3-6, it certainly is linking regeneration with the reconciliation/peace with God.
"But now apart from the law the righteousness of God has been made known, to which the Law and the Prophets testify.
This righteousness is given through faith in Jesus Christ to all who believe. There is no difference between Jew and Gentile, for all have sinned and fall short of the glory of God, and all are justified freely by his grace through the redemption that came by Christ Jesus." Rom 3:21-24
"Is this blessedness only for the circumcised, or also for the uncircumcised? We have been saying that
Abraham’s faith was credited to him as righteousness. Under what circumstances was it credited? Was it after he was circumcised, or before? It was not after, but before! And he received circumcision as a sign, a seal of the righteousness that he had by faith while he was still uncircumcised. So then, he is the father of all who believe but have not been circumcised, in order that righteousness might be credited to them." Rom 4:9-11 (righteousness after faith but -before- circumcision, see Rom 2:29 on our circumcision of the heart by the spirit)
"It was not through the law that Abraham and his offspring received the promise that he would be heir of the world, but through the righteousness that comes by faith.
For if those who depend on the law are heirs, faith means nothing and the promise is worthless, because the law brings wrath. And where there is no law there is no transgression." Rom 9:13-15 (Note that unbelievers under the law cannot be heirs - cannot be the born again children of God.)
Therefore, the promise comes by faith, so that it may be by grace and may be guaranteed to all Abraham’s offspring—not only to those who are of the law but also to those who have the faith of Abraham. He is the father of us all. As it is written: “I have made you a father of many nations.” He is our father in the sight of God, in whom he believed—
the God who gives life (quickeneth) to the dead and calls into being things that were not." Rom 4:16-17
"Yet he did not waver through unbelief regarding the promise of God, but was strengthened in his faith and gave glory to God,
being fully persuaded that God had power to do what he had promised. This is why “it was credited to him as righteousness.” The words “it was credited to him” were written not for him alone, but also for us, to whom God will credit righteousness—for us who believe in him who raised Jesus our Lord from the dead. He was delivered over to death for our sins and was raised to life for our justification." Rom 4:20-25
"Therefore,
since we have been justified through faith, we have peace with God through our Lord Jesus Christ,
through whom we have gained access by faith into this grace in which we now stand. And we boast in the hope of the glory of God.
Not only so, but we also glory in our sufferings, because we know that suffering produces perseverance; perseverance, character; and character, hope. And hope does not put us to shame, because God’s love has been poured out into our hearts through the Holy Spirit, who has been given to us." Rom 5:1-5
God's love poured out into our hearts through the Spirit certainly sounds like regeneration.
"Since we have now been justified by his blood, how much more shall we be saved from God’s wrath through him! F
or if, while we were God’s enemies, we were reconciled to him through the death of his Son, how much more, having been reconciled, shall we be saved through his life! Not only is this so, but we also boast in God through our Lord Jesus Christ, through whom we have now received reconciliation." Rom 5:9-11
Being saved through the life of Christ follows reconciliation, which follows justification, which follows faith.
"For if, by the trespass of the one man, death reigned through that one man, how much more will those who receive God’s abundant provision of grace and of the gift of righteousness reign in life through the one man, Jesus Christ!" Rom 5:17
Reigning in life through Christ certainly sounds like regeneration.
"..so that, just as sin reigned in death,
so also grace might reign through righteousness to bring eternal life through Jesus Christ our Lord." Rom 5:21
"We were therefore buried with him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father,
we too may live a new life.
For if we have been united with him in a death like his, we will certainly also be united with him in a resurrection like his.
For we know that our old self was
crucified with him so that the body ruled by sin might be done away with,
that we should no longer be slaves to sin— because anyone who has died has been set free from sin.
Now if we died with Christ, we believe that we will also live with him. For we know that since Christ was raised from the dead, he cannot die again; death no longer has mastery over him. The death he died, he died to sin once for all; but the life he lives, he lives to God
. In the same way, count yourselves dead to sin but alive to God in Christ Jesus. Therefore do not let sin reign in your mortal body so that you obey its evil desires. Do not offer
any part of yourself to sin as an instrument of wickedness, but rather offer yourselves to God as those who have been brought from death to life; and offer every part of yourself to him as an instrument of righteousness. For sin shall no longer be your master, because you are not under the law, but under grace." Rom 6:5-14
Dying with Christ that we might live in Christ? Dead to sin but alive to God in Christ Jesus? Brought from death to life? That all sounds like regeneration and being born again!
