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The steady-state, space-charge-limited piezoresistance (PZR) of defect-engineered, silicon-on-insulator device layers containing silicon divacancy defects changes sign as a function of applied bias. Above a punch-through voltage ($V_t$) corresponding to the onset of a space-charge-limited hole current, the longitudinal $\langle 110 \rangle$ PZR $π$-coefficient is $π\approx 65 \times 10^{-11}$~Pa$^{-1}$, similar to the value obtained in charge-neutral, p-type silicon. Below $V_t$, the mechanical stress dependence of the Shockley-Read-Hall (SRH) recombination parameters, specifically the divacancy trap energy $E_T$ which is estimated to vary by $\approx 30$~$μ$V/MPa, yields $π\approx -25 \times 10^{-11}$~Pa$^{-1}$. The combination of space-charge-limited transport and defect engineering which significantly reduces SRH recombination lifetimes makes this work directly relevant to discussions of giant or anomalous PZR at small strains in nano-silicon whose characteristic dimension is larger than a few nanometers. In this limit the reduced electrostatic dimensionality lowers $V_t$ and amplifies space-charge-limited currents and efficient SRH recombination occurs via surface defects. The results reinforce the growing evidence that in steady state, electro-mechanically active defects can result in anomalous, but not giant, PZR.