ZOMBIE INTUITIONISM: APPARENT LOGICAL POSSIBILITY VERSUS APPARENT EXPLANATORY IMPOSSIBILITY

Why not just jettison preoccupations with "conceivability" and (apparent) "logical possibility" and focus instead on the real problem, which seems to be explanatory impossibility. That's an epistemic, not an ontic matter.
For whether zombies are or not possible, we appear to be incapable of explaining (in the usual causal/functional way) how and why they are or are not possible.

And that's the real (explanatory) gap that speculations about Mary or the Contrary cannot fill...

Because, if we are content to let provisional ignorance serve as our criterion for logical possibility, then both the truth and the falsity of the Goldbach conjecture are as logically possible as tachyons, magnetic monopoles or free quarks until one or the other is proved.

(I am expecting a rebuttal from Kripke Schematicians...)