You're right, I absolutely agree about the race thing. The Constitution was interpreted to mean slaves were other persons, but nowhere does it actually define who qualifies as an "other person".
What the Constitution literally said is that 3/5 of "all other persons" would be counted for representation and tax apportionment. To interpret this as a judgment on the person-hood of individuals is both misguided and beyond the scope of a literal reading. The passage does not say "non-persons" or "half-persons." It says "other persons," as distinct from free persons, indentured servants, or Indians not taxed. Speaking of Indians, they were only counted if they were taxed. By your reading, the Founders considered taxation as essential to person-hood. I guess that may be possible, but I've never heard of that.
My first problem is the creation of two political categories of person: one free, one "other". Merely by creating that distinction, other persons are implicitly less than free.
Non-citizens are deprived of some freedom in this political system, since they're denied the right to vote and certain legal rights, but that's okay because they belong to a different political system. Indians not taxed, likewise, are non-citizens, beyond the scope of the U.S. political system; their lack of representation in the U.S. political system is due to their adherence to a separate political system, rather than a judgment by the government about their personhood.
And if a lower rate of representation makes someone less of a person, how about voting? Is the age requirement for voting a denial of children's person-hood? Or did nineteenth-century Americans believe that women were not persons? Not that I am aware.
In many ways children are not people. They cannot vote, they cannot make all their own choices, but just as felons can petition for restoration of rights, minors can request emancipation. And they become enfranchised automatically at the voting age.
Felons are stripped of legal rights of personhood through a hopefully equitable legal process, one in which they have equal standing (again, hopefully) as anyone else.
Free blacks and women inhabited a grey area: they were either by law or custom denied voting rights in many cases. However, they could avail themselves of the legal system to some degree; they were not formally considered property in all respects, except if they were married: that's more a condemnation of the historical nature of the institution of marriage than it is on the mores of the time.
So, Free Blacks and Women were more than 0/5 of a person, but less than 5/5. Putting a number on how free they are would be a subjective exercise in futility, and would vary depending on state and local laws and social standards. Women may have been worse off, because as far as I'm aware they were explicitly not permitted by law to vote, except in New Jersey for 1-2 decades if they were unmarried; in other respects, they were less than equitably treated, being denied property rights if they were married, for instance. But with Blacks their disenfranchisement was more a social standard, if I understand correctly, which I suppose dwindled in the North as the civil war approached. Free Black Women who were married must have been very low on the totem pole of legal equity, though, about as close to slaves as one could be.
Slaves, on the other hand, never achieved freedom automatically through adulthood, and were not stripped of their freedom through any equitable legal process. They could not vote or sue in court.
Slaves were openly declared property by the courts. What else could the country have done to further reduce its estimation of slaves as human beings? I don't think there's anything more it could have done, thus slaves were effectively 0/5 of a person, as judged by the government.They were no less
inherently people because of their lack of political rights, but I disagree with your statement that "other person" status was not a judgment on the part of the nation: The United States judged them to be not-people in the only way it could: by denying them legal rights, in court, and by denying them political rights, at the polls. Without either one of those, all other rights, such as freedom of speech or the RKBA, were meaningless, because they could be, and were, deprived those rights arbitrarily, with no recourse.
I agree that the government cannot and does not make judgments about the inherent worth or sentience of individuals. It can pretend to, but all it can really do is grant them rights or not. By failing to grant those rights, I think it judged slaves to be non-humans.