First of all, I am surprised to see you appealing to non-biblical sources. Aren't you the one who constantly mocks those who quote authors and commentaries, and prides himself on relying only on the Bible?@Martin Marprelate
A small sampling from those in the PST camp that do:
“…In the third item of this marvelous prophecy reference is made to a double bruising, the woman”s Seed shall bruise the Serpentï”s head, and the Serpent should bruise His heel. The last clause in this prediction has already become history. The bruising of the heel of the womanï”s Seed is a symbolical reference to the sufferings and death of our Savior, who was wounded for our transgressions and bruised for our iniquities….”
A.W. Pink A. W. PINK COLLECTION GLEANINGS IN GENESIS
“…His sufferings and death; pointed at in Satan's bruising his heel, that is, his human nature. And Christ's sufferings are continued in the sufferings of the saints for his name. The devil tempts them, persecutes and slays them; and so bruises the heel of Christ, who is afflicted in their afflictions. But while the heel is bruised on earth, the Head is in heaven….”
Matthew Henry Genesis 3:15 Commentaries: And I will put enmity Between you and the woman, And between your seed and her seed; He shall bruise you on the head, And you shall bruise him on the heel."
“…thou shalt bruise his heel—The serpent wounds the heel that crushes him; and so Satan would be permitted to afflict the humanity of Christ and bring suffering and persecution on His people….”|
Jamieson-Fausset-Brown Genesis 3:15 Commentaries: And I will put enmity Between you and the woman, And between your seed and her seed; He shall bruise you on the head, And you shall bruise him on the heel."
“…If it be applied to the Seed of the woman, Christ, his heel may note either his humanity, whereby he trod upon the earth, which indeed the devil, by God’s permission, and the hands of wicked men, did bruise and kill; or his saints and members upon the earth, whom the devil doth in diverse manners bruise, and vex, and afflict, while he cannot reach their Head, Christ, in heaven, nor those of his members who are or shall be advanced thither….”
Matthew poole Genesis 3:15 Commentaries: And I will put enmity Between you and the woman, And between your seed and her seed; He shall bruise you on the head, And you shall bruise him on the heel."
And I will put enmity between {o} thee and the woman, and between thy seed and her seed; it shall bruise thy {p} head, and thou shalt {q} bruise his heel.
(o) He chiefly means Satan, by whose action and deceit the serpent deceived the woman.
(p) That is, the power of sin and death.
(q) Satan shall sting Christ and his members, but not overcome them.
Geneva Study Bible Genesis 3:15 Commentaries: And I will put enmity Between you and the woman, And between your seed and her seed; He shall bruise you on the head, And you shall bruise him on the heel."
“…Jesus Christ died to put away sin by the sacrifice of himself, and to destroy him who had the power of death, that is, the devil. Thus he bruises his head - destroys his power and lordship over mankind, turning them from the power of Satan unto God; Acts 26:18. And Satan bruises his heel - God so ordered it, that the salvation of man could only be brought about by the death of Christ; and even the spiritual seed of our blessed Lord have the heel often bruised, as they suffer persecution, temptation, etc….”
Clarke's Commentary Genesis 3:15 Commentaries: And I will put enmity Between you and the woman, And between your seed and her seed; He shall bruise you on the head, And you shall bruise him on the heel."
“…Thou shalt bruise his heel — The part which is most within the serpent’s reach, and on which, being bruised by it, the serpent is provoked to fix its venomous teeth, but a part remote from the head and heart, and therefore wounds there, though painful, are yet not deadly nor dangerous, if they be observed in time. Understood of Christ, the seed of the woman, his heel means, first, his humanity, whereby he trod upon the earth, and which the devil, through the instrumentality of wicked men, bruised and killed;…”
Benson Commentary Genesis 3:15 Commentaries: And I will put enmity Between you and the woman, And between your seed and her seed; He shall bruise you on the head, And you shall bruise him on the heel."
“…The seed of the serpent would bruise the heel of the seed of the woman. On the cross Satan bruised the heel of Christ, causing His death. Bruising suggests something that was not ultimate or final. Christ died on our behalf being made sin for us (2 Corinthians 5:21). He bore our judgment upon Calvary's cross and, in doing so, bruised His heel. Though wounded, the damage done to Jesus was not final, for He came back from the dead three days later….”
What Does Genesis 3:15 Mean?
“…Satan was integral in the betrayal, arrest, torture, and execution of Jesus. During Jesus’ final meal with his disciples, Satan entered into Judas to betray Jesus (Jn. 13:2, 27; Lk. 22:3). Revelation 12 tells us that Satan couldn’t wait to get his hands on Jesus, so that he could “devour” him (Rev. 12:4)….”
Why Did Satan Crucify Jesus? | Evidence Unseen
“…It was at the cross that Jesus was bruised. Yes, it was in the purpose and plan of God. Yes, it was God letting His Son be punished for our sins. Yes, it was the just wrath of God. But at the same time it was Satan who was inflicting these bruises. The sufferings of Christ on the cross was His bruise. And as I said, it healed very fast. It only took a few hours before Jesus said, “It is finished,” and in triumph gave His life up.
This bruise served the purpose of God. Sure, it was inflicted by Satan, because Satan was the source of sin. Satan was the source of the corrupt world system. Satan was the tempter who plunged the whole human race into sin. So in a great way, Satan is responsible for all of this. Therefore he’s responsible for the bruising of Jesus, even though it’s within the framework of God’s judicial purpose….”
https://www.masters.edu/thinking_blog/bruised-heel-crushed-head/
My position on this question has come from preaching through Mark 14 and 15, especially on Gethsemane, our Lord's arrest, trial and crucifixion which I did before Easter this year. As I prepared the sermons, it became clear to me that all Satan's efforts were directed to keeping our Lord from dying on the cross. All the commentaries that I consulted made no mention of Satan 'murdering' Christ, but rather concentrated on Christ resisting temptation and remaining faithful to His mission. I have presented the Scriptures several times already, so I won't do so again.
One last point. You quote Arthur Pink from Gleanings in Genesis. I have the book. This is one of his earliest writings and he makes IMO several errors it it. One is his reliance on the 'Gap Theory.' Another is his Dispensationalism, of which he publicly repented a little later. I have his main works concerning the Atonement: 'The Satisfaction of Christ,' 'The Doctrine of Reconciliation' and 'The Seven Sayings of the Saviour from the Cross' - the works of his maturity. In none of them can I recall seeing any mention of Satan murdering or crucifying Christ. I am not aware of any public recantation of his comments which you quoted, but nor am I aware that he ever repeated them.
However, you should not suppose that I am denying that Satan 'bruised the heel' of our Lord. I just agree with several of the people you quote that the wound was not deadly. Satan was constantly attacking Him, either by direct temptation or by using others to do so (e.g. Matthew 16:22-23), but the temptation is not to go to the cross, but to avoid it.