Kinetic molecular memristors offer a compelling path toward high-density analog in-memory computing by achieving 14-bit precision, wherein discrete redox transitions and counterion displacements dictate non-volatile conductance across a deterministic energy landscape. However, integrating these nanoscale kinetics into macroscale circuit simulators has remained bottlenecked by derivative discontinuities and solver convergence failures. Here, we present a physics-inspired continuous kinetic model that bridges microscopic molecular transport with scalable circuit architectures. By casting discrete intramolecular states, counterion relaxation dynamics, and Marcus-Hush-Chidsey electron transfer rates into continuously differentiable state variables, we derive a robust, Spectre-compatible compact model and a matching vectorized Python solver. This work culminates in a unified computational platform to reliably predict the behavior of complex circuits built on these molecular memristors.