Canted antiferromagnet α-Fe₂O₃|Pt bilayers offer a platform for multistate memory, but spin Hall magnetoresistance (SMR) readout cannot distinguish states separated by 180^∘, limiting detection to three states. We show that a field-like perturbation lifts the degeneracy of opposite states in α-Fe₂O₃, enabling the resolution of six states in the SMR signal. We introduce a dual-modulation SMR method to mitigate thermal drifts and enable reliable readout. Computations of first- and second-harmonic SMR reveal the role of exchange, anisotropy and field-like perturbations in resolving the states.