That’s the thing. I don’t see how they can find him not guilty on one charge and guilty on the other. If it is self-defense, then he can’t be guilty of either charge and that it the only defense he has.
The only way they could justify doing that is by rejecting self-defense.
And to reject self-defense, they have to reject the fact that the burden of proof is on the prosecution to prove Z did not act in self defense, not on Z to prove he did.
Hypothetically speaking, they could find it wasn't proper self defense but that Z didn't have the "depraved mind" necessary for murder 2.