The flux of high-energy protons slow-extracted from the CERN Super Proton Synchrotron (SPS) is limited by the induced radioactivity caused by the beam loss intrinsic to the extraction process. Methods to substantially increase the efficiency of the extraction process are of great interest to fulfill requests for an increasing flux of 400 GeV protons to the present experiments, located in the North Area of the SPS, and also for potential future experiments with very high demanded protons on target. A crystal shadowing technique to significantly reduce the beam scattered and lost on the electrostatic extraction septum during the third-integer resonant slow extraction process has been developed and a prototype system tested with beam. The technique is based on the use of a thin, bent silicon crystal to coherently channel or volume reflect the portion of beam that would otherwise impinge the wire array of the electrostatic septum and instead eject it into the transfer line toward the production targets of the experiments. In this paper, the concept is described and applied to the SPS machine in order to specify the requirements of the prototype crystal shadowing system. Beam dynamics simulations of the prototype system are compared and benchmarked to the results obtained through beam tests, before being exploited to understand the characteristics of the present system and the potential performance reach of an optimized, future operational configuration. The remaining challenges faced to bring the system into operation, the optimization possibilities and other potential applications are discussed.