The correct way to parse this is ….
The thing that he should is the whereby . That is, he should do something about that demeanor of his where anyone would immediately know what he is thinking. The grammatical content of the fan-translation is essentially correct here.
Your translation has all the right components, but it puts them together in a sort of incoherent way. In particular, Hisui is not directly saying that she knows what Shiki is thinking (though it's implied, obviously).
* * *
Addendum: I can't quite tell from your translation where you're getting tripped up on translating this, so maybe this breakdown will help.
* = "what [Shiki] is thinking"
* = "for [someone] to immediately know what [Shiki] is thinking"
* = "an attitude/demeanor whereby [someone] immediately knows what [Shiki] is thinking" (let us call this entity "X")
* X = "to alter X"
* X = "it is better to alter X"
* X = "I think you ought to alter X"