Sounds interesting, but I have doubts about utilitarian arguments too. Why not check out Rothbard's "For a New Liberty"? It's in audio form for free here:
https://mises.org/media.aspx?action=category&ID=87
Chapter 12. The Public Sector, III: Police, Law, and the Courts is particularly impressive.
EDIT: Here is Rothbard's amusing argument against utilitarianism:
"Let us consider a stark example: Suppose a society which
fervently considers all redheads to be agents of the Devil and therefore to be executed whenever found. Let us further
assume that only a small number of redheads exist in any generation—so few as to be statistically insignificant. The utilitarian-libertarian might well reason: “While the murder of isolated redheads is deplorable, the executions are small in number; the vast majority of the public, as non-redheads,achieves enormous psychic satisfaction from the public execution of redheads. The social cost is negligible, the social, psychic benefit to the rest of society is great; therefore, it is right and proper for society to execute the redheads.” The natural-rights libertarian, overwhelmingly concerned as he is for the
justice of the act, will react in horror and staunchly and
unequivocally oppose the executions as totally unjustified
murder and aggression upon non-aggressive persons. The consequence of stopping the murders — depriving the bulk of society of great psychic pleasure — would not influence such a libertarian, the “absolutist” libertarian, in the slightest. Dedicated to justice and to logical consistency, the natural-rights libertarian cheerfully admits to being “doctrinaire,” to being, in short, an unabashed follower of his own doctrines."