I present the results of an optical design study into the performance benefits of non-rotationally symmetric “freeform” gradient-index (GRIN) media on a pupil-relay head-mounted display. A range of design variants are presented based on freeform-GRIN lenses consisting of ternary base-material combinations that are enabled by recent developments in additive manufacture. The optical performance of these designs is compared to homogeneous solutions comprising combinations of spherical, aspheric, toric, and freeform surfaces. I show that freeform-GRIN media represent powerful degrees of freedom for aberration correction in tilted and off-axis optical systems, performing comparably to homogeneous freeform optics while illustrating significant potential reductions in lens count and mass.