First one should prove that slavery is inherently morally bad. While there are some aspects of slavery which we tend to estimate as negative, slavery as institution had its place and solved many societal problems of its time. For example, it is an acceptable alternative for state welfare for society which deem welfare to be ethically bad. There is another advantage: legal slavery make slavery and associated problems explicit, while in so-called modern free societies an allegedly "free" (wo)man is treated as state slave de-facto while poor guy/girl thinks s/he is free. For example, many modern state obligate parents to allow their children be indoctrinated in state schools. Also if parents do not conform to numerous rules, imposed by the state, it can take their children away. It is very similar to slave breeding, but unlike slavery where this system is open, in modern state this slave system is sugar-coated and a regular citizen is often harbours delusion that he is free. So, on the contrary, we might conclude that slavery is in some aspects is more sincere and honest about some unpleasant sides of reality.
And as your starting point on slavery being inherently morally wrong is not proven, your following arguments are not necessarily correct as well.