This is a wonderful article. I find that we often can't even get to discussing some of the details of how a liberated society would function with such issues because people cannot even get their heads around one tenth of what you are saying.

I think that it's important to note that courts and jurisprudence have existed since before our current brand of governments and it would be feasible to still have courts to help enforce private property rights so long as individuals consented to the use of such a form of arbitration. In your BP example, the company might have preferred to submit itself to the mercy of a sound but independent court rather than to feel the wrath of the free market and at the same time, the free market could still function in dishing out punishment if it was not satisfied with the court's intervention.