Your analysis misses a major point.
Once that hammer shows up Arbery's status changes from "jogger" to "escaping armed criminal". A hammer is a formidable weapon. Lethal against anything short of a projectile weapon.
Plus if he has discarded the hammer, what even more potent weapon has he retained?
It validates the decision to bring weapons in the first place, and justifies carrying the shotgun out of the truck.
RE: A hammer is a formidable weapon. Lethal against anything short of a projectile weapon.
You still don’t shoot to kill a person with the hammer (assuming he was holding it while running), unless he is throwing the hammer at you ( and we don’t know that ), tailing him BY CAR while using your cell phone to call the cops is still the right option.