A piezoelectric, continuously twisted, structurally chiral medium (PCTSCM) is a reciprocal medium whose constitutive properties vary helicoidally along its axis of spirality. After using a transformation that effectively grafts oblique propagation on axial propagation, the exact analytic solution for oblique propagation in a general PCTSCM is obtained as a uniformly convergent matrix polynomial. This attractive form will allow a comprehensive assessment of the utility of PCTSCMs for novel transducers.