All three Persons of the Godhead were involved in offering up Christ as the sacrifice. So, in some senses the whole Godhead is typified in the High Priestly work but in different senses. However, only the Father is attributed as the actor with the intent, design and acheiver in providing the sacrificial body (Heb. 10:5-9) and working the circumstances for making the sacrifice actual while the Son performs a role characterized by submission to the will, and providential determination by the Father. He did not nail himself to the cross but submitted to it. Thus, the Son offers himself up by the role of submission. The Holy Spirit enables Jesus to submit to that role. So the Holy Spirit offers Christ up through enabling Christ to submit for that end. However, it is the role of the Father that characterizes the High Priest more so than either the Son or the Holy Spirit because the Father is given the credit for the intent/purpose and working the circumstances that actually acheive it.
Him, being delivered by the determinate counsel and foreknowledge of God, ye have taken, and by wicked hands have crucified and slain: - Acts 2:23
I am not aware of any system that believes that the Father descended into some kind of bodily form and was the actual person condemning Christ to the cross and then actually taking a hammer and nailing Christ to the cross. Pilate was not willing to condemn or crucify him until pressured by the Jews. The Roman Soldiers actually beat him and then nailed his hands to the cross. However, if Acts 2:23 means anything, it means that it was no accident that Christ was slain by such wicked hands but that God purposed it so. "Determinate counsel" cannot possibly mean anything less than the cross or death of Christ was due to purposeful determination by God. John 3:16 and the act of God giving his Son had this purpose in view. Jesus said for that very purpose he had come into the world when his disciples denied that he would go to Jersulem and be crucified. It was not man's purpose that he was fulfilling.
Ro 8:32 He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give us all things?
1Jo 4:10 Herein is love, not that we loved God, but that he loved us, and sent his Son to be the propitiation for our sins.
2Co 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
Lu 15:23 [The Father commanded] And bring hither the fatted calf, and kill it; and let us eat, and be merry:
Isa. 53:10a Yet it pleased the LORD to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin,
In all the above cases it is the Father that is credited with being the Actor while the Son is credited with being the object of the Father's action. The only sense that the Son can be credited with that action is in a submissive role.
Isaiah 54:10 states clearly that it was the Lord that bruised "him" and it was the Lord that "shalt make his soul an offering for sin". Hence, The Lord is clearly stated to be the antitype of the High Priest that kills, binds and offers up the sacrifice on the altar for the sins of the people. He "sent HIS SON to be the propitiation for our sins" and "HE made him to be a sin" offering for us and "HE spared not HIS SON." It is the Father that is doing this because the one it is being done to is repeatedly called "HIS SON." Of course, HIS SON is a WILLING party to this and so the Son came to do the will of the Father with regard to the cross, and thus offered himself up willingly. But in the eternal purpose of redemption the Father is the one giving HIS SON for that end, the Father is the one that provided the body to be sacrificed and it is the Father giving, and OFFERING up His Son for that end, The Father is the one pleased to bruise him and make his soul an offereing for sin. The Son is willing for this to be done and does not resist.
Hence, the party that provided the sacrificial body and purposed it to be sacrificed and used the hands of wicked men to accomplish that predetermined end typified by the High Priest's action is the Father not the Son, as the Son simply came to do the will of the Father - "I come to do thy will O God." He laid down his own life only in the sense of submission to the revealed will of the Father that he be the sacrificial lamb the Father would give, or would offer up to be the propitiation of our sins. He offered himself only in the sense of submission to the revealed will of the Father Who sent him to be the sacrificial lamb. But it is the Father that determined that end, purposed how it would be accomplished and brought it to pass and who is credited with making that offering or giving His son for that end.
The Father purposed it and brought it to pass. The Son submitted to the Father's will. The Holy Spirit empowered Christ to do it. Hence, all three Persons of the Godhead were actively involved in making this offering, but intent, design and purposeful action in accomplishing this offering is credited to the Father while the Son is characterized in a submissive role in passively allowing himself to be offered. The Holy Spirit's part is enabling Christ to willingly submit to this role as he offered himself up by the power of the Spirit. So, the Father fits the type of the High Priest more than either the Son or the Spirit as the determination, design and accomplishment in bringing about that offering is credited to the Father.
So, all three Persons of the Godhead typify the High Priest in various degrees. The Son was the offerer in the sense of submission, thus offering himself in that characterization. The Holy Spirit was the offerer in the sense of enablement to make the offering. However, it is the Father's role that dominates both roles of the Son and Spirit as the roles of both the Son and Spirit are SUBMISSIVE to the role of the Father who is repeatedly characterized as the One who purposed, provided and acheived making the sacrificial offering actual.
So yes, my view of God is consistent with my view of Christ's Person and the fullness of deity incarnate without confusion of deity with humanity. My view of God is consistent with God's redemptive purposes, roles and provision of full atonement.