We consider stacked intelligent metasurfaces (SIMs) as a tool to improve the performance of bistatic integrated sensing and communications (ISAC) schemes. To that end, we optimize the SIMs and design a radar parameter estimation (RPE) scheme aimed at enhancing radar sensing capabilities as well as communication performance under ISAC-enabling waveforms known to perform well in doubly-dispersive (DD) channels. The SIM optimization is done via a min-max problem formulation solved via steepest ascent with closed-form gradients, while the RPE is carried out via a compressed sensing-based probabilistic data association (PDA) algorithm. Our numerical results indicate that the design of waveforms suitable to mitigating the effects of DD channels is significantly impacted by the emerging SIM technology.