In trying to sort out the question of the incarnation and divine omniscience, we're mixing together several ingredients. First, we throw in the biblical texts which say a) Jesus is God; and b) Jesus' knowledge was limited. Then, we mix in the divine attributes, including omniscience. Finally, we mix in our philosophical attempts to understand the ins and outs of the Trinity--and since philosophy is rational and since our reason is often faulty, we should expect some uncertainties in this endeavour.
Some ingredients simply don't mix well, and maybe they shouldn't be thoroughly mixed together. I'm not sure. But the point is that it is going to be hard to make all the data fit with each other.
1) Jesus is God
2) God knows everything
3) The Bible speaks of Jesus' knowledge being limited
4) Somehow the first three points fit together without contradiction
In all this, we should fully embrace the incarnation. Jesus wasn't born fully aware that Mary must eat protein in order to produce the stuff in her mammary glands which would deliver milk from her breasts into his stomach if he capably sucks her nipples, and that his body would produce waste which would soil the clothing rags which Zach the merchant sold to her ten years ago as a blanket. (Forgive me if this is a bit crude--I hope not.) He didn't lie there in her arms sucking her breast and thinking, "Oooh, the pizza she ate last night is a bit spicy."
But by the time he was 12, he did have a sense of his special and unique relationship with God so that he could refer to him as MYFather."
This understanding of his special relationship with God as his Father was confirmed to him by the voice from heaven at his baptism: "This is my Son, whom I love, with him I am well pleased." The divine revelation propelled Jesus into the wilderness to contemplate his mission. Yes, indeed, he was God's Son, but the question remained, what kind of Son would he be?
In the baptismal declaration, the divine voice cited passages from Gen 22 (God telling Abraham to take his son, his only son whom he loved) with a Suffering Servant passage in Isaiah. The implication here is that Jesus as God's Son would be the Suffering Servant who would be offered up as a sacrifice; for (as in Gen 22), God himself would provide the sacrifice. The time in the wilderness was a time of contemplation and meditation on the baptismal declaration, and Satan tempted him along those lines: "If you are the Son of God, then...."
All this suggests that while Jesus understood himself as having a unique relationship with God as his Father, Jesus did not have a clear vision of his ministry until about age 30 when he was baptised. The plea at Gethsemane then was a genuine plea that another way would be made manifest.
More remarkably, Jesus' faith in God was a real faith--not one based on the omniscient knowledge of final outcomes. In his full humanity, he trusted God with his life, holding fast to his belief that God would raise him on the third day. Not being omniscient, Jesus allowed himself to be arrested, beaten, mocked and crucified. Not being omniscient, he cried, "My God, my God, why have you forsaken me." Not being omniscient, he could only put his faith in God, as reflected in his final cry, "Into your hands, I commit my Spirit."
This is our God, the Servant King.