Strain engineering is a promising method for next-generation materials processing techniques. Here, we use mechanical milling and annealing followed by compression in diamond anvil cell to tailor both the intrinsic and extrinsic strain experienced by technologically important pyrochlore oxides, Dy2Ti2O7 and Dy2Zr2O7. Raman spectroscopy, X-ray pair distribution function analysis, and X-ray diffraction were utilized to characterize atomic order over a wide range of spatial scales at ambient conditions, providing a comprehensive picture for understanding the high-pressure structural response. Raman spectroscopy and X-ray diffraction were further used to interrogate the material in situ at high pressure. The high-pressure structural behavior is found to be dependent on the sample’s initial atomic order, defined by its crystal structure, concentration of cation anti-site and anion Frenkel defects, and internal strain. Overall, it is shown that properly tuning a material’s initial defect profile can lower the critical pressure of the phase transformation, and enhance the transformation’s kinetics, without sacrificing significant mechanical integrity.