The use of an intense ultrashort laser pulse to induce electron polarization has been proposed previously in the literature. We used Python to reproduce the local constant crossed-field approximation (LCFA) in order to calculate the transverse polarization obtained from repeated laser interactions, starting from nonzero initial polarization, as well as the associated energy kicks. We also studied how the collision geometry affects both the magnitude of ${\chi }_e$ and the effective field asymmetry experienced by the electrons, identifying several possible ways to generate useful asymmetry even when the laser wavelength does not admit pulse lengths that directly reach the plane-wave optimum. We show that, over multiple laser shots, lower values of the quantum efficiency parameter ${\chi }_e$ are associated with higher transverse polarization output, but require a greater number of shots to reach saturation. We also show that the mean energy loss scales approximately linearly with ${\chi }_e$. Based on this framework, we developed a preliminary BMAD laser module to simulate the full 6D dynamics in a proposed FCC-ee Z pole lattice and to identify the threshold ${\chi }_e$ value above which particle losses begin to occur.