There are two big problems with your position. Well, more than two, but the two that jump out at me are:
1) Georgia law is
quite clear and specific on the subject of justification for use of deadly force: an individual is not justified in using deadly force if he or she was the initial aggressor, unless he or she attempted to withdraw and the other person pursued. (This is, as I understand it, a fairly typical provision in self-defense law.) Arbury was not the initial aggressor. McMichael was. QED, McMichael can't claim justification.
2) Georgia law at the time was also quite clear and specific on whether or not a private citizen could make a citizen's arrest: a citizen's arrest was legal only if the citizen directly witnessed the suspect commit a crime, or had "immediate knowledge" that the suspect had committed a crime. I've seen nothing that suggests Arbury committed any crime the day he was killed, so the McMichaels can't have witnessed one. At most they were justified in calling 9-1-1 and following Arbury until an officer arrived.
Bottom line: there is no provision of Georgia law that justifies McMichael shooting Arbury. That makes it murder.