We present comprehensive results from constant NVT and constant NPT Monte Carlo simulations of particles interacting via a biaxial variant of the Gay-Berne potential which we term the Internally Rotated Gay-Berne (IRGB) potential. The IRGB potential may be considered to be a single-site approximation to the interaction between two zig-zag shaped molecules, the extent of this molecular biaxiality being characterized by an internal rotation angle delta. We find that increasing the value of delta frustrates the formation of orientationally ordered phases, all phase transitions being shifted to lower temperatures and higher densities. Additionally, for delta greater than or equal to 30 degrees, the smectic B phase is replaced by the tilted smectic J phase. The smectic A phase, in contrast, is destabilized completely for sufficiently large delta, with neither smectic A nor its tilted equivalent, smectic C, being observed. This suggests that models for smectic C-formation which are based on biaxial intermolecular attractions may not offer the best route to obtaining this phase.