Deep salt–gypsum formations undergo pronounced creep under high temperature and nonuniform in situ stresses, transferring time-dependent loads through the cement sheath and causing casing ovalization. The constant viscosity of the classical Nishihara model limits its ability to simultaneously represent weakly activated and strongly nonstationary creep responses. An exponentially time-varying viscosity was therefore introduced into the Bingham viscoplastic branch and coupled with a reference-normalized Heard factor to develop a nonstationary Nishihara–Heard model. Five 8 h triaxial creep tests at a confining pressure of 30 MPa, with deviatoric stresses of 15–65 MPa and temperatures of 25–90 °C, were used for multi-condition parameter identification. The proposed model increased the pooled R² from 0.582 to 0.907 and substantially reduced systematic medium-to-late-stage residuals under strongly activated conditions while retaining the near-stationary response under weak activation. The model was implemented in Abaqus/Standard through a user material subroutine (UMAT) and coupled with a casing–cement sheath–formation finite-element model. Calibration using well X1 reproduced the measured one-year casing ovality, and fixed-parameter predictions for wells X2 and X3 yielded relative errors below 8%. These results demonstrate preliminary cross-well engineering applicability within the investigated 1–2-year observation window.