I explain it (IMO) by saying that God is immutable which is the say the three members of the Trinity are immutable (premise 1).
I appreciate you trying to explain "forsaken" from the Hypostatic Union framework. But what you need is an actual Scriptural definition. What we can say that forsaken doesn't means separation. That's what I always argue against in PSA topics. Did the Father forsaken the Son, no, in the sense of separation as most PSA suggest. But what sense was he forsaken? According to Biblehub:
to abandon, desert (ἐν equivalent to ἐν τίνι, in some place or condition), i. e. to leave in straits, leave helpless, (colloquial, leave in the lurch): τινα, Matthew 27:46 and Mark 15:34
In other words, the Father is still there with the Son according to the Divine Nature. The inseparable union of the Trinity (John 8:29, 16:32). But based on this unique particular condition (the cross), the Father is not going to offer help (Matthew 4:6), even though, the Father is still there with the Son (Psalms 22:1 and 24). The Father even listened to his cry for help and he was heard because of his reverent submission (Hebrews 5:7-8). This is for the sake of us and our salvation (Luke 22:42), so the Son was left helpless in that particular circumstanial condition and had to suffer through it. Again, the Father is still there with the Son by doing the work of atonement (Hebrews 9:14). Nothing more needs to be added to the definition of "forsaken" like how some people include: randomly quoting verses, emotional despair, separation, and spiritual death, etc.
The forsaken (turning of God's back) is the relationship of the divine nature to the human nature (premise 2); there was no longer a connection (forsaken) between the two natures from the human nature's point of view (conclusion).
I disagree. Based on the definition of "forsaken" is not suggesting a relationship between the two natures as if there was no longer a connection. The two natures are inseparable in the union by the Son. According to the human nature the Son was helpless in the circumstance. The Son 'could' according to the Divine Nature use omnipotence. Since there is no off and on button. By jumping off the cross, instantly healing himself, and zapping everyone dead. Thus, the Son saved himself from death. But that wasn't the purpose of the one will (the divine will of the Father is technically the divine will of the Son, John 6:38, Hebrews 10:7, Matthew 26:39), instead the Son used omnipotence in a different way (1 Corinthians 1:18, 24, 2:8).
Your example below is not how communication of attributes works.
Just like the human nature of Christ did not know the time of his coming because the divine nature of Christ did not communicate it to the human nature. In effect, this knowledge was "held back" (forsaken) from the human nature.
No. I understand the argument you are trying to make. Most Hypostatic Unionists would see this particular argument as being a straw man, ridiculous and absurd. That the Son as God is omniscient according to the Divine Nature doesn't lack knowledge by any logical means.
The Son did not know the day and the hour from his humanity, he did know it in his humanity. Because he is the Son as God in the flesh (or 'Deity exist in bodily form'). He doesn't restrict his knowledge as God, but the Son as God is omniscient and knows the day and hour in his humanity.
The Son does know but choose not to make it known to us. For example, the apostles was curious about a particular time of the Son's return: "that day or hour no one knows (eidó)," (Mark 13:32) during the Son's post resurrection his apostles asked again for a specific time: "It is not for you to know (ginóskó) the times or dates" (Acts 1:7), this carries the idea that the Son knows but choose not "to make known or to reveal" to his apostles. Its not meant for them to require such information that the Father placed in his own authority.