Optical coherence microscopy (OCM) provides non-invasive, label-free, cellular-resolution imaging based on optical scattering contrast. Its interferometric detection captures the optical field, providing opportunities for computational reconstruction. However, the depth coverage of OCM is restricted by defocus and photon collection, and its penetration depth is limited by multiple scattering (MS). Here, we propose integrating hardware and computational adaptive optics in different ways, to improve the throughput, penetration depth, and contrast of volumetric OCM. This hybrid adaptive optics (hyAO) approach splits the image formation process into a combination of hardware and computation components. For sparse sample imaging, we generated astigmatism using hardware adaptive optics (HAO) to achieve a more equalized photon distribution across depth, and removed the applied aberration (and defocus) via computational adaptive optics (CAO). We applied this hyAO method to perform 3D time-lapse imaging of in vitro fibroblast cell dynamics over a 1mm×1mm×1mm field-of-view with 2μm isotropic spatial resolution and 3-minute temporal resolution. The hyAO approach is not only beneficial for high-throughput volumetric imaging, but is also capable of suppressing MS/speckle. For scattering sample imaging, HAO was used to illuminate the sample volume with diverse aberrated point spread functions to decorrelate the MS/speckle fields, and CAO was applied to computationally mitigate the resolution penalty of these intentionally induced aberrations. By imaging with this aberration-diverse OCT using 12 volumetric reconstructions, we achieved a 10 dB enhancement in signal-to-background ratio at a USAF target plane beneath a scattering layer (7.2 scattering mean-free-path), and a 3× speckle contrast reduction within the scattering layer.