The MC is the ONLY person who knows he made the decision to kill Carter. Carter was disarmed but not "immobilized". He had not stopped fighting and was resisting. He had not surrendered. The appropriate response, by law enforcement, is to fully subdue him. Generally that would be accomplished by a choke hold, in this case the choke hold broke Carter's neck.
The MC has committed no crime. He was fighting to defend his life and the lives of Emma and Charlotte. His story, which is true as far as it goes, is that he was attempting to subdue Carter and Carter died as a result. This is a clear case of self defense, and given he's wounded, bleeding, and was unarmed against a knife there is no case for excessive force.
The MC admits only to intending to stop the threat, while fighting for his life. BTW. That's exactly what he tells Charlotte and Emma. If either ask him about it he maintains that he was fighting to stop Carter. That protects them and him. Charlotte can only testify that the MC and Carter were fighting and that Carter was killed in the struggle. She can not testify that he intended to kill Carter because she does not know that for a fact.