An interesting chain of reasoning, but the golden rule is itself a moral decision (you don't have to live by the golden rule – and many don’t) and thus it cannot be used as an a priori premise to get a necessary conclusion. Unfortunately too, even if it could, the slaveholder can still maintain his (or her) belief in the golden rule by asserting exactly what you pointed out -- that a slave is a non-person and doesn’t count -- provided the slave is sufficiently different in race, culture, etc. to be not like the people the slaveholder cares about. You and I think slavery is a very bad thing, but I don’t think you can write an a priori proof of a moral position. If all you want to prove is that slavery is incompatible with a universalized interpretation of the golden rule, then you are saying more-or-less what I have already argued – that slavery is incompatible with the enlightenment concept of equality. That far, we agree!