If you'll forgive my saying so, you've got it exactly wrong. An inalienable right is one that can't be consented away; that's the definition of "inalianable". Your understanding is the self-contradictory, you're saying that something can only be inalienable if it can be alienated. You may disagree that there are inalienable rights, but you can't take them to be alienable.
Your description already produced a government that would consider suicide illegitimate, -- hardly a government rooted in liberty.
It's not clear what Locke would've thought. His argument against suicide was the same as his argument against murder, that both you and others belong to God, and as such should live on the Earth as long as He pleases, with just punishment for crime the only reason a person could rightly kill someone. He cited the commandment to Noah after the flood, "Whoso sheddeth man's blood, by man shall his blood be shed," to show that his one reason for killing someone was authorized by God, and therefore didn't contradict his argument from God's ownership. What I don't know is whether or not Locke regarded suicide as a crime in the Earthly sense.
Of course, my understanding doesn't contradict the dictionary meaning, since under my definition no one other than the right holder can contract it away. The essence of freedom is though that whatever is mine as a right I can do as I please with, includeing foreswear it. Would you comment on property rights and their unalienability?