I would honestly say that when you look at anything you cannot avoid having a knowledge of God at the same time. When you look at another human being, the moment you say 'I know that there is a person in front of me' you also 'know' in an innate sense that the person was created by God.
But this would have to be unconscious to the point that it would only ever be acknowledged (even for a believer) when pointed out. I don't look at my friend and go "Oh, a human being created in the image of God" and start thinking deep theological thoughts. Instead I say, "Oh, it's Luke." You don't do metaphysics when you greet someone. Metaphysics is what happens when we realize that there is a problem between two different ways of acting ordinarily.
So as long as they remain slaves to sin, their perspective will never be correct on anything.
Not true. Atheists know all kinds of stuff. Are you suggesting that an atheist plumber doesn't know how to fix the pipes. For someone who doesn't know anything, he sure fixed them well.
false knowledge
Ok, this is a contradiction in terms. No one can have false knowledge, given that knowledge is warranted true belief.
The unbeliever attempts to 'know' things apart from 'knowing' God, and all that results is that he has false knowledge.
Again, this is a contradiction in terms. You either know that X or you don't. There's no middle ground here. Again, you're equivocating on the word "knowledge" and it's resulting in all kinds of confusion. Please define what you mean exactly by "knowledge" here.
Knowledge has nothing to do with having a coherent system of belief and everything to do with how you ended up believing something.
It just seems like you are so against the transcendental argument and presuppositional apologetics.
a) They aren't in Scripture.
b) The TA is so cumbersome as to be practically useless.
c) Very often they ignore ordinary usage and common sense in favour of logical coherence. Frankly, when you start going around saying ridiculous things like "unbelievers don't actually know anything," it's hard to take you seriously (Charlie has given a fuller analysis of this, so I won't go into it further).