On the 'know how it feels to not know' point, the main issue is that by analysing our brains, it still doesn't know how it feels as it would know what that person does not know, hence it cannot know how it would feel to not know. It's a subtle difference, but relevant for an omni-trait. Also, on the paradox, the point was there's ultimately a stalemate: one side assumes omniscience is impossible, one side otherwise, and there's no reason to lean either direction.
If our feelings are ultimately the result of brain states then it would know what that person was feeling emotionally as well as exactly what it did not know. I think you are unknowingly advocating a kind of dualism under which there an omniscient being can get the facts of the matter, what specific information is lacking, but our personal feelings would be unavailable through inspection. However even supposing such a system was right, if a being knew everything about the physical world as well as all of the activity of our mental life it would know exactly what we felt at any moment and what that experience was like.
As for my proposed problem with omniscience: I’m not just assuming omniscience is impossible, I made an argument. Now that argument can stand or fall but it isn’t an assumption. I certainly didn’t begin with the conclusion that omniscience was impossible and work backwards rather I worked forward from what it would mean to know all things and attempted to illuminate an example where it just isn’t possible to know the truth about reality. If I succeeded there’s good reason to abandon the idea of omniscience. If in the face of this argument all one has is the assumption that omniscience really must be possible anyway there’s very good reason to lean away from it being possible. Otherwise all logical arguments would be pointless.
I will say, stepping back from my argument about omniscience, the bigger problem lies in the silliness of attempting to apply absolutes to terms of relativity. It just doesn’t make any sense to say a being is maximally tall or infinitely witty as these terms are ultimately grounded in comparison. Why should I think any differently of terms like just, powerful or knowledgeable? Moreover “knowledge” of our world is (largely) acquired after effort and the idea of a being that just innately knows everything is an affront to how we think of knowledge. Such all-everything traits might have once sounded impressive but it seems to me they are all just as ridiculous as claiming a being is all-charming.
Thanks for the dialogue.