As you know, I reject some aspects of penal substitution. But there is surely an element of substitution. Is 53 shows Jesus as being wounded for our transgressions. I don't accept the narrative of PSub, that God had to punish someone in order to be able to forgive us. But still, the way God chose to take away our sins did involve Jesus taking them on. 1 Pet 2:24.
I consider Rom 6 to be the most detailed treatment of the atonement in the NT, though the Words of Institution are also fairly explicit.
Rom 6 says that Jesus' death deals with our sin, but not quite that it does so by bearing our punishment.
That's Ro 3:25-26, where the punishment due on the sin of the OT was temporarily passed over until it was paid in the atoning sacrifice of Jesus.
Through union with him in faith, he takes our sins, and dies to free us from them. Paul explains that death releases from sin. Hell isn't in view here. Because we are united with Christ, and thus he had our sins, his death releases us from them. And through him we are raised to new life. Because it involves his taking our sins, it is substitutionary, in my view.
Releasing us from sin is only part of the purpose of Jesus' death.
As far as I can see, the atonement doesn't have to do with forgiveness at all. God is perfectly capable of forgiving sin, and has done so in the past (Rom 3:25).
It was definitely about forgiveness in the OT (Lev 4:20, 26, 31, 35, 5:10, 13, 16, 18, 6:7, 19:22; Nu 15:25, 26, 28).
It was definitely about forgiveness in the promise of the new covenant of Jer 31:34.
And it's definitely about forgiveness in the NT.
"This is my blood of the covenant, which is poured out for many for the forgiveness of sins." (Mt 26:28)
And Paul makes clear in Ro 3:25-26 that all God's forgiveness of sin, past, present and future, is only because of the atoning sacrifice of Jesus, and that punishment on the sin of the OT was passed over until Jesus paid the penalty for them.
There is no forgiveness apart from Jesus' atoning sacrifice.
"Without the shedding of blood (death--penalty for sin), there is no forgiveness." (Heb 9:22)
The other moderately explicit explanation of the atonement is the Words of Institution. Jesus speaks of his blood as the blood of the new covenant. This is only explicit because of the OT context. The new covenant is surely the covenant of Jer 31:31, which writes the law in our hearts. That's completely consistent with all of Jesus' preaching, which sees that the way to change people is to change their hearts.
What then is the blood of the covenant? It is the covenant sacrifice.
The "blood of the covenant poured out for forgiveness of sin" is Jesus blood poured out, which is his poured-out life (
death).
God's unilateral unconditional New Covenant to forgive sin and remember it no more (Heb 8:12) was possible because of Jesus'
atoning sacrifice for that sin (2Co 5:21).
My understanding of the OT sacrificial system is that it is basically a sacrament,
This has no basis in Scripture, starting with the word "sacrament."
where giving a sacrifice is a visible sign of repentance and commitment to change.
The sin sacrifices were
penalties for sin, not signs (Lev 5:6, 7, 14, 6:6).
A covenant sacrifice would be a visible sign of the commitment to keep the covenant.
So Jesus' atoning sacrifice is simply a visible sign of his keeping the covenant?
So I believe that Jesus saw his death as an act of vicarious repentance
This has no Biblical basis.
You are confusing the repentant heart which offered the atoning sacrifice with the atoning sacrifice itself.
The sacrifices were
penalties for sin which, when offered
with a repentant heart, atoned (paid) for the sin, which was then forgiven.
and commitment to the renewed covenant, on behalf of his people.
First of all, the New Covenant is unilateral, not bilateral.
His people do not keep the covenant of their Surety.
Nor was the New Covenant a "renewal" of the Old (Sinaitic) Covenant.
It was "not like the covenant I made with their fathers." (Jer 31:32).
It was a new, never-existing-before covenant.
The
Sinaitic covenant with Israel was
conditional, based on keeping the law.
The
New Covenant is
unconditional, pure grace, with those who believe in Jesus Christ.
This is at least implicitly substitutionary. In repenting on behalf of his people, he is taking on the responsibility for their sins.
In taking on the responsibility
of their sin,
and in dying
for their sin,
you have presented Jesus paying the penalty for their sin.
That's penal substitutionary atonement.
So why the need to present his sacrificial atonement as simply "sign"?
In all the NT discussion, e.g. the OT analogies, it seems to me that Jesus died to save people, not to make them savable. Who did he save? His people. Look at the OT analogy. Did the high priest intercede for the Philistines? Of course not. He interceded for his people. Jesus interceded for his people, who Paul defines as those who have faith.
Agreed.