Improving the ionic conductivity of outstanding, composition-optimized crystalline electrolytes is a major challenge. Achieving increases of orders of magnitude requires, conceivably, highly nonlinear effects. One known possibility is the use of high electric fields to increase point-defect mobility. In this study, we investigate quantitatively a second possibility that high electric fields can increase substantially point-defect concentrations. As a model system, we take a pyrochlore oxide (La2Zr2O7) for its combination of structural vacancies and dominant anti-Frenkel disorder; we perform molecular-dynamics simulations with many-body potentials as a function of temperature and applied electric field. Results within the linear regime yield the activation enthalpies and entropies of oxygen-vacancy and oxygen-interstitial migration, and from three independent methods, the enthalpy and entropy of anti-Frenkel disorder. Transport data for the nonlinear regime are consistent with field-enhanced defect concentrations and defect mobilities. A route for separating the two effects is shown, and an analytical expression for the quantitative prediction of the field-dependent anti-Frenkel equilibrium constant is derived. In summary, we demonstrate that the one stone of a nonlinear driving force can be used to hit two birds of defect behavior.