Context. Debris disks ─ collisionally sustained belts of dust and sometimes gas around main sequence stars ─ are remnants of planet formation processes and are found in systems ≳10 Myr old. Millimeter-wavelength observations are particularly important, as the grains probed by these observations are not strongly affected by radiation pressure and stellar winds, allowing them to probe the dynamics of large bodies producing dust. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is analyzing high-resolution observations of 24 debris disks to enable the characterization of debris disk substructures across a large sample for the first time. Aims. For the most highly inclined disks, it is possible to recover the vertical structure of the disk. We aim to model and analyze the most highly inclined systems in the ARKS sample in order to uniformly extract the vertical dust distributions for a sample of well-resolved debris disks. Methods. We employed both parametric and nonparametric methods to constrain the vertical dust distributions for the most highly inclined ARKS targets. Results. We find a broad range of aspect ratios, revealing a wide diversity in vertical structure, with a range of best-fit parametric values of 0.0026 ≤ hHWHM ≤ 0.193 and a median best-fit value of hHWHM = 0.021. The results obtained by nonparametric modeling are generally consistent with the parametric modeling results. We find that five of the 13 disks are consistent with having total disk masses less than that of Neptune (17 M⊕), assuming stirring by internal processes (self-stirring and collisional and frictional damping). Furthermore, most systems show a significant preference for a Lorentzian vertical profile rather than a Gaussian.