"The claim of certain ignorance entails a claim of omniscience, which is self-refuting."
No, it's a fact. Right now there is no way to know if a God exists.
At least for those who have yet to leave this plane of existence. Those who have departed probably know.
What percentage of the total available knowledge do you claim to possess? You are claiming absolute certainty of the truth of the proposition that there is not enough knowledge to be able to determine whether or not there is a God. In order to make this claim with certainty you would have had to search throughout the entire universe, because of the possibility that knowledge of God might exist somewhere you haven't looked yet. You cannot possibly search everywhere since you are a finite being. Therefore, unless you are omniscient (or God Himself) you cannot be certain that that there isn't knowledge somewhere that you haven't looked yet. Therefore you cannot be certain that there is no way to know if God exists.
Cordially,