Do you think that John 3:16 will harmonize with John 6:38? I think that it does, but I interpret John 3:16 differently than you do. If you interpret the word "world" as meaning all mankind, will it harmonize with John 6:38 or with 1 John 2:15. Why would God tell us to not love a world that he says that he "so loves"? unless he is speaking of two different worlds? Thayer's Greek interpretation of the word "world" in John 3:16 is used of believers only, he also says it means the same in John 1:29, 3:17, 6:33, 12:47, 1 Cor 4:9, and 2 Cor 5:19. in This line of thinking, John 6:38, John 3:16 and 1 John 2:15 all harmonize.
I believe John 6 harmonizes with John 3:16, yes.
If we take your contention, that Jesus came to save only those whom Father God gave to him, then what of that Godly characteristic our Father is said to possess, Omni-Benevolence?
God does all things for the zeal of His own glory. God predestined all things, as we're told throughout the scriptures. If we go with your proposal about Jesus saving only those our eternally knowledgeable Father planned to give him prior to the creation of the world and wrote those names in the Lamb's Book of Life, then what would be the point of Proselytizing? Going forth, as Jesus commanded his Disciples, to bring the Good News to all the world when God, who was Jesus, had already predetermined by name only those persons who would be saved by His free gift of grace.
This would also necessitate the contrary. That God had predetermined before the world came into being by His creative will those who would die in the state of damnation, or sin, that had not yet come into the world because God had not yet created the first people to begin that process under the Law of God given first in Eden.
God being a superior intelligence, laying out all who would come to Christ and giving them to what is essentially Himself as that Savior, would have foreordained who would be saved throughout all time, and conversely whom would be damned. Which would make our part, repentance, unnecessary. Because God had , per your model, it all worked out as to who among the human race His sacrifice on the cross was meant to save.
When those names were in the Lamb's Book of Life before the world came to be, the names of those God meant to be saved, God being a superior power would have in every sense done it all prior to the creation of anything. And we in turn would have to do not one thing since God foreordained our Salvation was secured by name in that book.