How does a non-God Jesus sitting as King forever correct the rejection of God as King that began in Samuel's day?

How does a non-God Jesus sitting as King correct the rejection of God as King that began in Samuel's day and continues even now?

The “correction” of difference in Kingship lies in the nature of the person being the King, and in the type of Kingship or Kingdom.

"I saw in the night visions, and behold, with the clouds of heaven there came one like a son of man, and he came to the Ancient of Days and was presented before him. And to him was given dominion and glory and a kingdom, that all peoples, nations, and languages should serve him; his dominion is an everlasting dominion, which shall not pass away, and his kingdom one that shall not be destroyed." - Daniel 7:13-14

A similar idea was also conveyed by:

"The Father loves the Son and has given all things into his hand." - John 3:35

This Kingship given to Jesus seems a different Kingship as the Kingship which was given to Saul, David and their successors. You reason that because Jesus says that his kingdom is not of this world, that David’s Kingdom was not of this world also. However, it seems that Jesus wants to make clear to his audience that his Kingdom is different from the Kingdoms that they are familiar with like the Kingdom of David. Nevertheless, Jesus is a successor of David and fulfills the promise that the descendants of David would Rule over Israel forever (2 Sam 7:16), But why could the type of kingdom not change? And become bigger, longer, and better?

Also, all other successors of David were mere human Kings, which eventually died, by which their Kingship ended (naturally), while Jesus will never die. Furthermore:

"Then the end will come, when he hands over the kingdom to God the Father after he has destroyed all dominion, authority and power. For he must reign until he has put all his enemies under his feet. The last enemy to be destroyed is death. For he 'has put everything under his feet.' Now when it says that 'everything' has been put under him, it is clear that this does not include God himself, who put everything under Christ. When he has done this, then the Son himself will be made subject to him who put everything under him, so that God may be all in all." 1 Corinthians 15:24-28.

As you also already noted, human Kings such as David and his earthly successors were placed in their relative positions by God, and they were not higher or even equal than God. The question uses the word "proxy" which means with the authority to represent someone, as has the flavor of "substitute". Although human Kings like David had authority given by God, it seems doubtful that any imperfect mortal human being were given so much authority that they could come even close to "represent" God. If an executive appoints a manager over some group of people, the manager is supposed to act in the interest of the executive, but that does not automatically imply that he/she "represents" the executive, the manager does not necessarily have equal or authority as the executive. Likewise, King is a position of relative authority, not necessarily representation. With Jesus this was rather different, because about him it is clearly written that he represents God. So this is another change in the King and type of Kingship, that can 'solve' the problem of God being rejected.

The last scripture also indicates that Jesus himself is subject to God. Furthermore, these and other bible verses also seem to indicate quite clear distinctions between Jesus, the son of man, the Son or the Lamb, and YHWH, God Almighty, the Ancient of days, the Father, also in their respective heavenly positions.

1 Samuel chapter 8 makes it clear that the desire for a human king was a denial of the covenant relationship with God who had pledged to be the saviour and deliverer of His chosen people. Israel broke the covenant and rejected God as their sovereign King. They wanted a human king.

The covenant in question is the conditional Adamic covenant. Adam was required to obey God in order to secure God’s blessing. When Adam broke the covenant by going his own way and disobeying God, he rejected God as his ruler, his King. This act of disobedience brought sin and its consequences into this world. Likewise, the rejection by Israel of God as their King (related in 1 Samuel 8) is merely a formal manifestation of the fallen Adamic nature. It can only be rectified by God, in Christ, reconciling the world unto Himself. If Christ is king but is not God, then the problem remains: One has accepted a king other than God.

Psalm 45:6 says that God’s throne and God’s kingdom will last forever and ever. It is to be an everlasting kingdom. Yet in Hebrews 1:8-9, this prophecy is applied to the Son of God, proving his superiority over created angels. This intimates the deity of the Messianic (and Davidic) king.

1 Timothy 6:15 says that God is the blessed and only Ruler, the King of kings and Lord of lords, who alone is immortal. How, then is the title Lord of lords and King of kings applied to the Lamb? (Revelation 17:14)

Revelation 19:11-16 describes the rider on the white horse, called Faithful and True, whose name is the Word of God, wearing the name ‘KING OF KINGS AND LORD OF LORDS’. How can Christ, returning as Warrior-Messiah-King, be given this most holy of names?

Conclusion: Only God has the right to rule as King in keeping with His covenant. Only God can be King of kings and Lord of lords. No human, no created angel, no demi-god, no little-god, no false god, can replace the Lord God as King, as Ruler, as Saviour and as Deliverer of His chosen people.

To accept a substitute is to reject God. Only by accepting God as King can the wrong that was done when Israel wanted a human king can God’s sovereignty over His people be fully restored in His everlasting kingdom. It is at the name of Jesus that every knee will bow (Philippians 2:10).