You do realize that your "Anarcho-capitalist" solution describes the EPA's history. Precisely the moment when the US Government declared ownership of the Mississippi River, and all federal lands under its protection.
http://www.law.cornell.edu/uscode/text/33/652
http://en.wikipedia.org/wiki/Mississippi_National_River_and_...
Your solution is really called "internalizing the externality", and a near hundred-year-old analysis can be found in Coase's Theorem. http://en.wikipedia.org/wiki/Coase_theorem
Your solution requires "some entity" to create the concept of ownership, and then sell pieces of the shared resource to other people. You ensure that an owner exists for every part of the river, and then you get an economically optimal solution.
But WHO declares ownership? WHO enforces this ownership? If you believe in "private protection agencies" and "private courts", it is obvious that ownership of "The River" should be settled in the "private courts".
Eventually, you start building an entity functions exactly like the current US Government (except you use Libertarian friendly words to describe it). So please, describe to me a technique that isn't currently being used by the US Government to solve the problem of Externalities. Otherwise, you end up just describing our current Governing philosophy.