Upvoted. Thoughtful criticism, as always, /u/dominosci. Some thoughts:

This point first, since my other point became quite long when I tried writing it out:

Laws that put cigarettes behind counters out of sight do not forbid you from buying them. [...] In all these kinds of cases, choice is entirely preserved."

It's true that choice is entirely preserved for consumers, but the liberty-restricting aspect of these paternalistic laws is that sellers are punished for putting cigarettes up front, offering large soda cup sizes, etc.

(I don't think anyone has the right to prevent these sellers from doing these things (unless, for example, the sellers are leasing the property from someone else and that legitimate owner made them agree to not put cigarettes up front (etc) as a condition of leasing the property).)

If you find nudging paternalism problematic, even though it is choice-preserving,

So the sort of "nudging paternalism" you mention isn't completely "choice preserving" (contrary to what you say) in that it limits what choices the producers can make.

Second point:

the endorsement of paternalism is the only plausible way their theory of laissez-faire property is supposed to get off the ground in the first place

I'm not aware of anyone who is a libertarian because they are a paternalist. The foundation of my libertarianism (at the very least) is not paternalism, but liberal values. (Note that I see statist liberals as imperfect liberals in that they don't believe in equality of authority.)

Nozick’s way around this unsavory realization is the endorsement of paternalism

I haven't really read Nozick, so maybe he is an example of someone who defends libertarianism on paternalistic grounds. Although, just based on my reading of the brief passage you quoted, I don't see how that is the case. (Same for Locke.)

First, let me say that I think any proponent of any political philosophy who wishes to maintain "I don't want to make people 'worse off (sense 1)'" has a "problem" in that their assigning of some agents with rights (of any kind) necessarily makes everyone else "worse off (sense 1)".

There is no way around this "problem." This is just necessarily true. Nozick doesn't get around it.

What it appears you are saying Nozick does is define another sense of "worse off" / "better off" for which it can be true that assigning rights to people doesn't make others "worse off".

To use an extreme example, a proponent of an anti-rape political philosophy (call the proponent an "anti-rapist") who wishes to make it illegal for anyone to rape anyone else supports making everyone "worse off (sense 1)" in that they aren't free to have sex with anyone else without their consent like they would be in the absence of others not having a right to not be raped. Now, since this anti-rapist wants to maintain "I don't want to make people worse off," he defines a second sense of "worse off" / "better off" to use when saying these words. He says that people are "better off (sense 2)" in that others cannot have sex with them without their consent. The anti-rapist then claims that the amount "better off 2" that people are under anti-rapism is greater than the amount "worse off 1" that they would be. (Really, one cannot make this claim without appealing to more fundamental values.) The anti-rapist then concludes that people are "better off overall (sense 3)" under anti-rapism than they would be if people didn't have the right to not be raped.

What it seems to me that you are doing (with your interpretation of Nozick) is saying that Nozick thinks it's okay to support libertarian property rights despite such rights making people worse off in a sense analogous to sense 1 above, because people are better off in an overall sense analogous to sense 3 above.

Maybe this interpretation of Nozick (and Locke?) is correct, or maybe it isn't. It doesn't appear correct to me[1], but I don't have enough information to tell since I haven't read him.

In any case, I don't see how you could jump from a libertarian saying "I think it's okay to support libertarianism' rights assignments because people would be better off in sense 3 than they would be if no one had rights" to "libertarians should support assigning some agent non-libertarian right X because assigning the agent this non-libertarian right would make people better off in some new sense 4 than they would be under libertarianism." In fact, I'm pretty much certain that you can't just make this jump.

What I think you need to do is argue why your sense 4 is the "better off" sense that I "should" care about or really do care about and just don't realize yet. And to do that you have to appeal to some more fundamental values that I hold and show how I just haven't realized yet that supporting non-libertarian "paternalistic sense 4" right X is a better way to realize my values than libertarianism.

If you find nudging paternalism problematic, even though it is choice-preserving, then it should follow a fortiori that you find the hard paternalism of property even more problematic.

I disagree, for reasons that I hope are clear from what I said above. Specifically, I think you are using two different senses of "paternalism" here (not nudging vs hard, since, as I pointed out above, both make people "worse off" in some sense (nudging paternalism e.g. makes soda-sellers "worse off" than they would be if they could offer their customers large cup sizes), but just two completely different senses). You can't just say that one sense of paternalism is lesser than the other, so if one accepts the lesser then one ought to accept the lesser. This is that "jump" that I mentioned earlier. It's just not true that accepting some assignment of rights on the basis that they make people better off in some sense must mean that you should accept a different assignment of rights for the reason that they make people better off in a different sense.

But of course libertarians don’t seem to see it that way. This is because their core value is property, not liberty.

What would you say the political views of someone whose core value was liberty look like? I don't have any good guesses at your answer, and thus can't fathom what you think you are communicating by saying that libertarians' core value is not liberty.

Also, re: "libertarians' core value is property," I don't see what this conveys either. There are countless ways that one can assign rights to stuff (property) in the world. I don't see why the libertarian theory of rights should be considered to be the theory whose core value is "property." That seems like an unfair way to use words to advocates of other political philosophies. So I don't think of my core political value as "property." Rather, as I said in my first comment to you, I explain my support of libertarianism's particular rights assignments as the result of my adherence to more fundamental values. To communicate to you what these fundamental values of mine are: They seem to me to basically be what most people understand by the term "liberalism," with the exception that I think the belief in political authority is an illiberal belief, rather than a belief consistent with liberal values.

[1] Again, this is a fairly blind guess since I haven't read much at all of Nozick or Locke, but it seems to me that with the "Lockean proviso" statement saying that they won't want to make others "worse off" what Nozick and Locke really mean is something descriptive, not normative. Well, perhaps they also mean it normative too, in that they are describing their normative values. However, I think the purpose of the statement is really to help the reader narrow down set of descriptive realities or sets of actions in which Nozick and Locke believe that some action actually results in an agent acquiring new rights to previously-unowned property. For example, maybe there is some empty area which some individuals occasionally pass through on their way wherever. It appears to me that what Locke and Nozick are saying is that they don't actually support granting full ownership rights to the area to someone who builds a house in the area, even if they otherwise would, because others had been able to pass through before and in granting the house-builder full rights over the land they would be making these occasional travelers worse off.