It Can't Happen Here is, to my mind, the least compelling of the various choices. It's a cautionary tale about a fascist takeover of the United States, written shortly before World War II when fascist takeovers were new and popular. That makes it something of a "yesterday's tomorrow": it didn't happen and it certainly doesn't look like happening now, in contrast to Robert Heinlein's "If This Goes On—" which is more relevant now than when it first appeared in the 1940s. And the values it defends are not so much libertarian as democratic, with Franklin Delano Roosevelt as the exiled leader of the "Jeffersonian" party. It still has some value, but it's not the best cautionary tale for us. It's also somewhat diminished by Lewis's "plain folks" characterizations, which tend to undercut the seriousness of his characters' struggles.
Animal Farm is a classic warning against communism, and more powerful in some ways than 1984, which is already in the Hall of Fame. But it's not especially "futurist" or even "speculative": Its pigs taking over the farm are not fantasy characters in a magical world, but characters in a beast fable, which is not a fantastic genre. I'm not sure it's a suitable candidate for an award that normally goes to works of science fiction or kindred genres (fantasy, horror, utopia, dystopia, and so on).
A Clockwork Orange, on the other hand, is set in a dystopian future, though its only truly extrapolative sfnal element is the language it's written in: Nadsat, a Russian-influence teenage slang of a disintegrating culture. It's a brilliantly ugly literary work. And its message is relevant to libertarian concerns, with its warning against the use of psychological conditioning to reshape behavior and its underlying point that people who aren't free to choose evil also aren't free to choose good: their actions have no ethical merit.
I like better, though, "True Names," which really is a no-brainer for this category: It's a major and influential work by one of the best known libertarian science fiction writers now living, which didn't get the Prometheus Award back in the day largely because that award was for novels rather than novella or novelettes. "True Names" really prefigured the whole cyberpunk movement, with its hacker heroes struggling against the system and its virtual reality where programs are spells; I've occasionally wondered if the reason there wasn't a cyberpunk movement till Gibson's Neuromancer was that the system Gibson's protagonists fought against was Big Corporations rather than The State, thus appealing more to trendy leftism. (Though, to be sure, Neil Stephenson came out of cyberpunk and arrived at something a lot closer to libertarian views of the matter.)
Then there's the out and out fantasy to which Vinge alludes in his opening pages, with his lines about the Great Enemy: The Lord of the Rings. Not everyone thinks this is a libertarian work. I think it at least has strongly leanings that way: First, because its central thesis is that a magical object that grants unrestrained power over others is not merely corrupting but addicting, and that the corrupting effect is especially dangerous because it can tempt people through their desire to do good and help other people; second, because it portrays a society living in freedom, the Shire, clearly modeled on ancient Iceland, and says that the ultimate justification of war and warriors is to protect such societies. And if the Shire is in many ways an idealized Edwardian England, well, in a lot of ways, Edwardian England was a freer society than we have now.
But my favorite, and the one I'll keep ranking in first place till it wins, is "As Easy as A.B.C." This is just an amazing piece of fiction. To start with, Kipling wrote it before World War I, but it not only uses the devices for indirect exposition that John Campbell pushed on his writers in the late 1930s, but shows a complete mastery of them. Its imagined future seems to baffle a lot of people—I've heard it interpreted, for example, as a portrayal of a totalitarian world dictatorship—perhaps because Kipling condemns democracy in it; but John Brunner had it right (despite Brunner's own socialist views) when he said that what Kipling wanted was not a society less free than a democracy, but one more free. It's worth noting that when a farm girl in rural Illinois traps several high officials of the "world government" in a force field and then tries to run them over with a plow, their reaction is to blow out her fuses and leave, sending back a message advising her to spend the night in the cellar while they straighten things out in Chicago. To Kipling's future society, the symbol of democracy is a statue called "The Nigger in Flames," recalling the old democratic custom of the lynch mob. Literarily his technique is stunning, from the angry crowd spreading out and melting away as the first light of dawn reaches them, to the multiple repetitions of "And all that that implies," each time with a different emotional charge. I first read "As Easy as A.B.C." in my early teens, and every time I've read it since then, I've seen more in it.