that works with a negative 'doesn't know it' but not with a positive 'does know it'.
The question does even X know Y? Implies that X is somehow out of touch, and not knowing Y, but maybe they do - surprise!
The question Does even X not know Y? Implies we would expect X to know Y, but what if even X does not?
The question Doesn't X even know Y? Implies that X is stupid and doesn't know a lot of things, but can it be that they are so stupid that they don't even know Y!?!?
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The question Does X know even Y? Implies they are knowledgable about a lot of things, but Y is such a rare and mysterious subject that we would be surprised if they did but what if they do know Y!?!
There are a lot more nuances than your analysis admits, and one is the assumed inflection of the speaker.
Consider "Does anyone know Y?". Depending on how it is said, it could be either a straightforward question about whether anyone knows Y, or with an upward inflection on "anyone" it could mean "I doubt anyone knows Y, but it's possible someone does."
With that same inflection on a person's name, "Does even Person know Y?" has the same meaning as your "Does even X not know Y?"
