Here are some observations that we may consider together, brother.Quite; but it does not affect the central point of my post.
Guthrie notes that Hebrews 13:10 (quoting Lev. 16:27) forms the backdrop of Hebrews 13:11-14 and reiterates the interpretation of Christ as the Day of Atonement sacrifice. There are two parallels between Jesus’ sacrifice and that of Yom Kippur. First, “Jesus also suffered outside the city gate.” The old covenant sacrifices were taken outside the camp, so also Jesus was taken outside the city. The purpose of Jesus’ sacrifice was “to make the people holy.” The high-priestly offering of Jesus was, however, “through his own blood.” The passage is actually defending the superiority of that offering.
FF Bruce attributes the parallel of Jesus’ death and animals burned outside the gate to signify that Jesus died in order to “sanctify the people – bring them to God as worshippers purified in conscience – by means of his blood, the willing sacrifice of his life.
I think it fair to divorce the imagery of the scapegoat from the goat and bull sacrifice as this is exactly what the author of Hebrews does. The symbolism is not Jesus taking our sins outside of the gate to the tomb (he was actually crucified outside the gate), but that his is a superior sacrifice that sanctifies his people. Bruce has noted that Israel considered what was inside the gate as sacred, but what was outside the gate as profane and unclean. Yet Moses set the tent outside the gate. God was rejected in the camp of Israel and manifested his presence outside. What was formerly sacred was now profane and what was formerly common was now hallowed. Given the author's comments regarding the faith of Moses in Hebrews 11, and Moses considering "the reproach of Christ greater than the riches of Egypt," I think it may be a weak argument to highlight the fact that Jesus suffered outside the city.
So while I do not see a strong foundation based on Hebrew passage, or on the fact that Jesus was crucified outside the gate, I do grant that this is part and parcel of bearing our iniquities, which I also see in the scapegoat symbolism. I think that we may agree on much here.
The purpose of the scapegoat was that it symbolized the fact that both people and land had been purged from their iniquity, since the high priest made the confession of communal sin over the goat before it was driven into the wilderness. What the scapegoat offers a symbol that will find its fullest expression in Christ who takes away human sin by his death. It is vicarious in that the scapegoat, while set free, symbolically takes away the communal sin of Israel. Christ’s death, likewise, is vicarious in that he bears not his own but our sin. He suffered for us, and died that we might live. Jesus died in our place, instead of us.
The problem is that what these passages show is a sacrifice, and even propitiation. It shows Jesus dying, taking our iniquities, satisfying the demands placed upon us by our sin, taking away our sins, etc. But what it does not show is penal substitution. What you need to prove is more along the line of Abraham’s willingness to punish Isaac as an offering to God. I am not certain, brother, that an atoning sacrifice can legitimately be considered “punishment” (although “wrath” may be appropriate, and certainly suffering applies).
Penal substitution deals with imputed guilt, not necessarily a sacrifice for us but a state whereby Jesus is literally considered as guilty as us. Having imputed our sins on Christ, God then views him as guilty (although Jesus never sinned, God sees him as evil and unholy…as sin) and justly punishes him with by inflicting upon Christ our punishment for our sin. This is absent in both of your “proofs” thus far. All atonement theories affirm the “proof” that you attribute to penal substitution atonement.
If, however, you are just walking through a development of your case then I understand. This would be your second foundation towards penal substitution, not your second “proof.” Thus far, I think you could take the argument as developed here towards any theory of atonement as we have yet to leave common ground.
(Commentaries I referenced are: George Guthrie, Hebrews and F.F. Bruce, The Epistle to the Hebrews).