Premise 2 isn't mine, you're creating a straw man.
Then state your argument. If I have misrepresented you--which I do not believe I have--then it is likely due to lack of any clear argumentation in the OP.
You said, "God can't know if there is something that He is unaware of." Yet if God knows that he is existence itself by which all other things come to be, he also knows that nothing exists except Himself and what he has created. Therefore he knows that he is aware of everything which exists, and he knows that there is nothing he is not aware of (for the only things he is "not aware of" are things that necessarily do not exist). There is nothing which exists that God is not aware of; God is aware of all things.
My argument comes from the very definitions of the words "know" and "aware". It has nothing to do with whether something is human or not.
Knowledge and awareness are both necessarily defined (somewhat) anthropomorphically, and therefore it would seem that your "argument" is based in anthropomorphism. God's awareness and knowledge are not at all like our own. When we attribute knowledge to God we do so by analogy, and the knowledge we attribute is assumed to be infinitely
greater than human knowledge. Your attribution assumes that it is
equivalent to human knowledge insofar as it is thought to succumb to the same weaknesses of human knowledge. But it is not equivalent, nor can it be thought to succumb to the same weaknesses (both
a priori and according to the creation arguments I've put forward).
You're stating that God can know about things He does not know about, and that is illogical.
I'm stating that there is nothing God doesn't know because he is the creator of everything that exists. God knows that he knows all things, and that there is nothing which he doesn't know about.
I said "whatever other metaphysical ways can be imagined" right in the section you quoted, yet you somehow overlooked it and made a point about us being physical beings.
Nevertheless, you're still relying on anthropomorphism. Your basis is "metaphysical" ways of discovering knowledge about the world. God does not discover knowledge or come to knowledge at all. For the creator creation is known
a priori.
Ahh, the "God is defined as..." argument. You can't define God with a quality that is logically impossible. That's the point of the argument. You can't define God as being a round square either.
What logical impossibility have I supposed? Define it.
I have shown that it is logically possible to know that you know everything. It doesn't matter how much smarter than me God is, it is impossible to know everything. Knowing that there is nothing that you are unaware of is logically impossible.
You've
stated that; you've
asserted that. But you've by no means demonstrated it. An argument would be in order.
By all means I grant that it is impossible for a human to know that they know everything, or even to know everything. But you want to make the jump to God, and there is no rational inference that allows that jump.