Bazer & Ericson (1959) and Torrilhon (2002) exposit on the very detailed solution of the equilibrium jump conditions at length. To wit, the process of making certain the correct root is selected is not at all trivial. The current MHDJumpSolver.m routine does not perform any correctness checking beyond the existence of a shock solution at all.
Potential output solutions are confirmed to be multivalued outside of the strictly slow regime.