Classical nucleation theory (CNT) is a promising way to predictively model the submicrosecond kinetics of phase transitions that occur under dynamic compression, such as the suite of experiments performed over the past two decades on the solidification of liquid water to the high-pressure ice VII phase. Myint et al. [Phys. Rev. Lett. 121, 155701 (2018)] presented the first CNT-based model for these types of rapid phase transitions, but relied on an empirical scaling parameter in their transient induction model to simulate the lag time that occurs prior to the onset of significant formation of ice VII clusters in the system. To build on that study, we model the liquid water-ice VII phase transformation using a numerical discretization scheme to solve the Zel'dovich-Frenkel partial differential equation, which is a fundamental CNT-based kinetic equation that describes the statistical time-dependent behavior of solid cluster formation. The Zel'dovich-Frenkel equation inherently accounts for transience in the nucleation kinetics and eliminates the need for the empirical scaling factor used by Myint et al. One major result of this research is that transience is found to play a relatively small role in the nucleation process for the dynamic-compression time scales of the liquid water-ice VII experiments being simulated. Instead, we show that it is possible to properly model the lag time using steady-state CNT by making small refinements to the interfacial free energy value. We have also developed a new dimensionless parameter that may be applied a priori to predict whether or not transient nucleation will be important in a given dynamic-compression experiment.