Nonvolatile magnetotransport responses in a single magnetic material have generally not been expected to exhibit a large ON/OFF ratio, because they are usually tied to spin-orbit coupling and therefore remain relatively weak. Here we show, contrary to this expectation, that giant nonvolatile magnetotransport can arise in a single magnetic material through magnetoelastic reconstruction of nonrelativistic real-space transport paths. Using the two-dimensional antiferromagnet FePS₃ as a representative system, first-principles quantum transport calculations reveal that charge transport is strongly tied to its quasi-one-dimensional zigzag sublattice chains and, under suitable doping, can even become confined to them. Moreover, strain lifts the degeneracy among symmetry-related zigzag variants and thus reorients these transport paths through magnetoelastic coupling. As a result, both the longitudinal and transverse conductivities change dramatically, yielding a giant magnetoelastic magnetoresistance of up to 10⁴% and an energy-independent Hall ratio that far exceeds the spontaneous Hall ratios found in conventional magnets. These results establish a route to exploiting symmetry-related magnetic variants and their associated transport paths for reconfigurable, high-performance spintronic devices with large nonvolatile readout contrast.