You don't have a right to "freedom from harm" if that means not hearing any speech you don't like.
You do have a right not to be shot, but "gun ownership" by itself does not conflict with that right. Being shot by someone who owns a gun does, but then the rights violation is the shooting, not the gun ownership.
> If you don't think there's a right to freedom from harm that competes with those other rights, I don't know what to tell you.
Your position, that all rights are inherently in conflict with each other, means nobody really has rights; what you call "rights" are really just at the mercy of the legislature:
> The real work of governance and legislation requires carefully negotiating trade-offs between competing priorities in an ever-changing world.
No, the real work of governance and legislation requires protecting the basic rights that everyone has to have to have a free, civil society, and stopping there. A government that has more power than that has too much power.
Your position reminds me of the old saying: no one's life, liberty, or property are safe while the legislature is in session.
> The fact that positive rights are "leftist" in some parts of the world reflects a degree of deep ideological incoherence and immaturity in those parts, more than anything, I think.
It reflects a degree of deep ideological incoherence and immaturity on the part of leftists who advocate for such "positive rights", yes. That's a recipe for eternal conflict. Which is indeed what leftism of that variety leads to.