The "logic of the design argument", would be that one can come to a correct conclusion about God's existence with one's reasoning processes, *given what the argument is attempting to prove*. At first when you said that the unbeliever should be at liberty to use the same process of reasoning to conclude that the Designer of this half-good, half-bad universe is not holy, holy, holy", I thought you were bringing up the problem of evil. But on second thought, it seems you are granting God's existence (say from the design argument), and then asking how God could be all good if evil exists. At this point I would ask the unbeliever (theistic non-Christian lets say) what his standard of morality is? And I would argue God is the standard of morality, and therefore is by definition good (for if evil really does exist there must be a standard to judge it against). So the unbeliever could infer something from the evil that exists in the world, but it wouldn't be valid to claim God isn't all good (as there needs to be a standard to judge evil against).