I've clearly antagonized you. But my purpose was to defend hoppe and illustrate that your idea (which is a commonly held one) does not solve the problem of incentives. I find Hoppe (as in this case) is poorly understood. This is partly because there is a difference between the absoluteness of his written arguments, and his predisposition to sound reasonable, humorous, and accommodating to students and lecture audiences. Worse, he has picked up from his generation of libertarians, an affinity for ridicule.
RE: Common failure mode
It is a common failure of all people who presume from a fragmentary argument that they understand the premise being argued, yes. But this is not limited to libertarians.

It is a byproduct of 'skimming' (see Nicholas Carr). And of being human.
(But I don't think I err in this case.)
RE: Intellectual failure...
This is the phrase that drew my attention. It is not a mistake on his part. You are, and you repeat throughout your argument, condemning his position, which relies upon a search for a kind of absolute truth, with a pragmatic one which seeks immediate means. This is to compare apples and oranges, and to criticize the apple grower for the color of his fruit. It is a fallacious criticism.
I realize that you want to act with urgency. Hoppe is searching for the actual solution to the problem of government, because we do not know how to act in the shorter sense, unless we have such a framework for the longer sense. If he were to spend his time here I suspect that he would say "i'm not trying to do what you are trying to do" Because at the moment you seek a pragmatic solution, you are not seeking an ultimate truth about human nature. And that is "uninteresting."
RE: You missed the phrase "In the absence of eliminating government, the best approximation..."
I didn't miss it. I tried to illustrate that you were introducing competition (good) without solving the problem of bureaucracy (bad). First, Hoppe does not eliminate 'government' - an exclusive definition of property rights, and a judiciary that enforces them, is a government. It is a government of laws, not of men. A monopoly on the definition of property rights (a contract, or constitution) is in fact a government. Hoppe eliminates the state (a corporation), politicians (the layers of management teams) and bureaucracy (a labor force with a monopoly ) as an organizational model from government. By using competing insurance companies to provide services currently supplied by a monopoly, he recreates 'government' but he does so with government without monopoly, and without high(short) time preference. This has been the problem of institutions faced by human beings since we developed irrigation.
If opportunities were traded in a measurable currency, then this would be a much easier topic to discuss.
RE: Turn over to one man.
He doesn't say that. Only that the private government of monarchies was superior to that of the state because the monarchs had superior incentives. His argument is that the incentives of members of a monopoly government are counter to that of the ordinary people. Again, this is not a pragmatic solution. It is a statement about the nature of incentives in different organizations.
RE: I'm doing something similar.
But you are not solving the problem of incentives in a bureaucracy. .... Wait... perhaps its your use of language. Yes. It could be that you mean to say the more common form which is that 'laws must apply equally to all people and not be retroactive" when you say 'act as if all shareholders had one vote'. Again, I think you are missing the point, that if you were to create competition in management you would not solve the problem that each organization would still have the incentives of a monopoly bureaucracy. Until you return to rule of law and insurance companies, you just recreate the existing problems at smaller scale.
RE: immediate steps .... what people would actually sign.
Two things:
a) Hoppe's position is that there is no possible means of transition outside of total failure. The purpose of the anarchic research program is to supply people in the future with concrete answers, if and when they have an opportunity, as did American founding fathers, to implement them. I agree with the purpose of the program (I am a participant in it), but, I would agree with you that any increase in returning to our property rights under the english common law would be an improvement. For transitional strategy, Thomas Woods is the most popular advocate of transitional methods that are practical and low cost: the cheapest and easiest is to find one state that will nullify federal statues, and then for that to spread. This would allow the evolutionary development of the 50 states - some back to rule of law and property rights, and some away from them.
b) The anarchic research program is an intellectual one, which aspires to solve the problem of institutions that support the ability of people to voluntarily cooperate whether their ends are shared or opposed, while retaining property rights and the possibility that disputes over property and contract will be resolved by predictable and peaceful means.
Also please understand my purpose: I find that Hoppe is misunderstood more than any other libertarian philosophy. And he has solved a problem, the problem of incentives, that plato and millennia of descendants did not. So, I try to correct that misunderstanding when I find it.
-Cheers