Empirically speaking, theism could never be totally refuted since, as you pointed out, no one is omniscient.
However, putting that aside for a moment, there are certain logical reasons that the theist God could not exist. Some of the attributes of this alleged being are impossible. Take omnipotence as an example. Is God able to create something indestructible, that not even he could destroy or uncreate? Whether you answer yes or no, his omnipotence is refuted.
Or what about his omniscience? Can the theist God ask a question that even he can't answer? If he can, he is not omniscient. If he cannot, he is not omnipotent.
Is God omnibenevolent; a being of pure love? But who could he have loved before he created the Son and with him everyone else? More importantly, if this God was all alone in the beginning, how could he have developed a language that would have allowed him to conceptualize, reason and so be capable of creating a universe? Language is a social phenomena. A single, eternal God could not develop a language and without language, conceptual thought, reasoning, mathematics - everything this God would need to create anything - would be impossible for him.
Did God create the Universe - the universe being defined mathematically as the set of all things existing in space-time? But space-time itself defines existence. A being that that created space-time would have to exist outside of it and therefore, would ipso facto not exist.
You see, even though I may never be able to disprove theism using the scientific/empirical method, I can easily refute it using logic alone. The theistic version of God is no more possible than two and three adding up to six. That said, there could be a deist version of God or an entire pantheon of polytheist gods. I guess it all depends on how strongly someone defines their atheism.
I think molinism explain all your (good) points.
Are you familiar with molinism?