Keep in mind that self-defense claim or not, the state has to prove 2nd degree murder, a predicate of which is intent. The witnesses could be critical and Zimmermann's injuries are going to be hard to overcome. I still say that the way that the two of them became proximate to each other is the critical factor. If the state can show that Z went after the victim, then the chance for conviction increases. If not, well ...
By the way, what would normally be the lesser charges included in jury instructions?