Let me cut through all this red tape.
Do you believe that God himself always and forever abides by the law of non-contradiction?
I do not believe God ever contradicts himself, when properly understood. I would give an example.
Exo 33:11 And the LORD spake unto Moses face to face, as a man speaketh unto his friend. And he turned again into the camp: but his servant Joshua, the son of Nun, a young man, departed not out of the tabernacle.
Exo 33:20 And he said,
Thou canst not see my face: for there shall no man see me, and live.
Verse 11 says God and Moses spoke face to face as friends speak. Verse 20 appears to be a direct contradiction of verse 11, God says Moses cannot see his face and live.
How can both verses be true and no contradiction? I believe that when God appeared to men in the OT that he limited some of his attributes. In verse 11 God appeared as a man and Moses could look directly on his face and live. In verse 20 God is speaking of appearing in his "glory". In this form no man can look on God and live.
This seems to be what you cannot understand, God is able to limit himself. He does not appear in his glory. In this form he is not self-sufficient and needs to eat and sleep. He is not everywhere at once, and obviously he is not omniscient in this state.
Now, I believe while God appeared in this limited form on earth, that at the same moment he was in heaven and all powerful, all knowing, etc...
But your statement that it is illogical that God can both know all things and not know all things is shown false by scripture. As has been explained by HoS, it is logical because it is supernatural.
Jesus is God, and Jesus said he did not know the exact day and hour he would return. This is not the only time he was not omniscient. He did not know who touched him when the woman with an issue of blood touched him.
Luk 8:43 And a woman having an issue of blood twelve years, which had spent all her living upon physicians, neither could be healed of any,
44 Came behind him, and touched the border of his garment: and immediately her issue of blood stanched.
45 And Jesus said, Who touched me? When all denied, Peter and they that were with him said, Master, the multitude throng thee and press thee, and sayest thou, Who touched me?
46 And Jesus said, Somebody hath touched me: for I perceive that virtue is gone out of me.
47 And when the woman saw that she was not hid, she came trembling, and falling down before him, she declared unto him before all the people for what cause she had touched him, and how she was healed immediately.
48 And he said unto her, Daughter, be of good comfort: thy faith hath made thee whole; go in peace.
As you see, Jesus did not know who touched him when the woman with an issue of blood touched him, that is, unless you believe Jesus to be a liar.
Believe the scriptures Luke.