Well said.

Nozick actually asks at what point did you cease to be slave, if ever. The question assumes that you start in slavery. Aristotle would define this as "circular logic".

I have always been a fan of the Ancient Greeks in these types of logical arguments. Socrates would ask you to, "Define your terms" before either agreeing or disagreeing with a premise. In this case the question is, "How do you define slavery?" Once I know how you define it, I can begin to discuss at what point you cease to be one.

"Freedom", now that's another enormous concept. "At what point is a slave free?"
Tell what you define as freedom and I would say he is free (according to your definition), when his condition satisfies your terms.