First of all, slaves are people, not livestock. I assume this is obvious to all. Perhaps they were treated as poorly as livestock. But this does not make them livestock.
For one thing, people, unlike livestock, are capable of independently judging their own value. That’s not the only difference between the two, but it’s the one Marx will focus on.
From a capitalist perspective, if someone sets a price on your labor, that’s the end of the story. But historically, it isn’t. Time and time again, people have rejected price tags as a measure of value.
I mean, it’s literally happening right now. Women are paid less than men. Do women accept that they are worth less than men? No, for the most part they don’t. But if they have a different idea of what they are worth, that idea must come from somewhere. And the LTV suggests where they got this idea. I work 40 hours doing X, you work 40 hours doing X, so our work is actually worth the same. Regardless of what we were paid.
Why go to the effort of coming up with an alternate definition of “value”? Not to set prices. Rather, to explain why there is an armed mob outside your window screaming for your blood. Maybe the market will bear whatever salary you chose to offer women or slaves, but don’t be surprised when that market suddenly gets burned to the ground. And at that point, nobody will care about any justification you may offer that is based on supply and demand, or the will of God, or the natural superiority of white males.
When that day comes, your economic system is over. And as far as Marx is concerned, it’s a matter of when, not if.
Your fundamental assumption is that people will be satisfied with the capitalist definition of value, because it is the basis for an orderly economic system. Whereas Marx assumes that people will reject it because it feels unfair, even if rejecting it results in economic chaos.