When I invite people to imagine the zombie world, this is not because once they believe that they can do so, this belief (about their imaginative capabilities) is evidence for anything. Rather, it's the fact that the zombie world is coherently conceivable that is the evidence, and engaging in the appropriate act of imagination is simply a psychological precondition for grasping this evidence.

If someone were to claim the following, would they be making the same point as you are making?

"The non-psychological fact that 'SS0 + SS0 = SSSS0' is a theorem of Peano arithmetic is evidence that 2 added to 2 indeed yields 4. A psychological precondition for grasping this evidence is to go through the process of mentally verifying the steps in a proof of 'SS0 + SS0 = SSSS0' within Peano arithmetic.

"This line of inquiry would provide evidence to the verifier that 2+2 = 4. However, properly speaking, the evidence would not be the psychological fact of the occurrence of this mental verification. Rather, the evidence is the logical fact that 'SS0 + SS0 = SSSS0' is a theorem of Peano arithmetic."