Our Big Fight Over Nothing: The Political Spectrum Does Not

I picked up on that and I think its going to limit the cogency of your criticism. The fact is few internet keyboard warriors actually read the primary literature. At best, they may read a few articles that introduce these ideas. But you're not going to get a rigorous understanding of anything by simply reading introductory pieces. You have to dig in and read the classics to really understand these ideas. Adam Smith is necessary. So is Menger and Mises and Hayek. And that is not easy reading. But it is rewarding even if you aren't a libertarian. There is a lot in these authors that should appeal to everyone who is interested in politics/economics and social orders. Its not one-dimensional. Its not "individual good, governments bad" type arguments. 

As for the various sub-types, I doubt I would be able to give an exhaustive list but I will point out a few.

You can generally decompose libertarianism into left and right libertarians. Benjamin Tucker and his libertarian socialist - market anarchist tradition is one strain and many people carry this tradition on today. The folks at C4SS like Kevin Carson would be working in this tradition. They published "Markets Not Capitalism" & "The Iron Fist Behind the Invisible Hand." Both are required reading in my view because they help inoculate right libertarian types from believing that capitalism evolved in a context of purity and freedom. 

Also on the left are Georgist Libertarians, or the folks who follow the ideas of Henry George, specifically his single tax proposal. 

Right and left libertarians also tend to break ranks on discussions of scientific method. Right libertarians tend to follow Mises and Rothbard and Hoppe and they pushed a method of economic theory firmly rooted in deductive reasoning and logic, almost completely devoid of any role for data, observation, experiments and testing. Left libertarians who studied under Don Lavoie, Peter Boettke and others at GMU are much more eclectic in their method and have followed Hayek into flirting with post-modern doubt about the merit of pure reason and abstract deduction. They have developed a brand of economics rooted in economic fundamentals but also informed by surveys, data, experiments, games and on the ground work in the field. And they are moving beyond pure economic theory, looking at how culture impacts economic decision making, how communities respond to crises and disaster, and how behavioral insights can inform economics. Vernon Smith is the big name there. He married behavioralism with Adam Smith and Hayek in his Nobel winning work in experimental economics. These academics have consciously followed the postmodern themes that were latent in Mises and have incorporated it in a more explicit manner. These postmodern libertarians are folks like Deirdre McCloskey, Don Lavoie and Chris Sciabarra. Ludwig Lachmann is considered by some to be one of the originators of this left turn in libertarianism. Rothbard says it is nihilistic (a refutation of truth, or the ability to know it at all). I think he's mistaken. 

On the right, you have paleos like Rothbard, Rockwell, Hoppe, Woods, etc. They are mainly centered in Auburn at the Mises Inst. These folks have a war brewing with the Koch funded libertarian groups, such as FEE, Cato, IHS, GMU, etc. Its largely a cultural thing. The Mises Inst folks wanted an alliance with the right and pushed a more conservative version of libertarianism to make the alliance work and poach conservatives into the movement. This is why the Ron Paul newsletters demonized young black men, gays, AIDS research, and immigrants. The rest of the movement wasn't having it and a little civil war started. Its still brewing and periodically a new skirmish breaks out.

A recent movement split that you may or may not heard of involved Jeffrey Tucker leaving the Mises Inst and publishing his important article about libertarian brutalism, thick vs thin conceptions of liberty. He saw the limits of the "thin" approach that was being pushed by the right libertarians. Essentially, the idea the thin people promote is that if a person does not initiate violence or support the initiation of violence, he can be as much of a bigot as he wants and still be a libertarian. All that matters to libertarianism is the NAP and whether or not naked force is being used. Ergo a covenant community of people who cut off gays and minorities from associating could still be considered libertarians.

J Tuck and the thick libertarians pushed back and argued that liberty would not thrive in a culture of hate and separation. In short, libertarianism cannot be a "liberty for me and not for thee" doctrine without undermining the context that makes liberty possible- the open and plural society. Tucker argued that libertarianism is necessarily liberal. And I think he won the day. 

I also want to mention the Ostroms (Lin just won the Nobel) and their work on community resource management. Before them, we thought in dualistic terms: private property or communal property (which suffers from a tragedy of the commons). The Ostroms showed how community resource management strategies emerge, bottom up, using empirical research, and then busted the narrative that private property was necessary to solve the commons problem. That's huge. And its left-wing.

There is a new group on the scene, the "Niskanen Center." Brink Lindsey, an ex-Cato analyst, started this new think tank and situated it in DC so as to be close to the action. They promote "state-capacity libertarianism" which basically means small government is not the goal, effective government is. The rest of the liberty movement tends to see these folks as too friendly with the state, essentially forgetting about the dispersed cost/concentrated benefit problem. They seem to deserve the moniker "belt-way libertarians" that was previously laid at the feet of the Cato Institute. 

To wrap this up, I hope I have made it clear that libertarians are not a monolith and that the struggle between left and right, liberal and illiberal, which characterizes so much of politics, is also a struggle that features prominently in libertarianism itself.

Arguably, the complex and difficult mashup of Liberalism and Conservatism that finds its home in the UK Conservative party is the reason for its remarkable success over 2 centuries and its constant internal warfare.

These two distinct political/philosophical positions are unified and get all the votes for both. The remaining positions- centre left, hard left, Christian Democrat (your "liberals") and various Nationalists share the remaining votes and rarely get to form a Government.