X-ray computed tomography (CT) is a crucial tool for non-invasive medical diagnosis that uses differences in materials' attenuation coefficients to generate contrast and provide 3D information. Grating-based dark-field-contrast X-ray imaging is an innovative technique that utilizes small-angle scattering to generate additional co-registered images with additional microstructural information. While it is already possible to perform human chest dark-field radiography, it is assumed that its diagnostic value increases when performed in a tomographic setup. However, the susceptibility of Talbot-Lau interferometers to mechanical vibrations coupled with a need to minimize data acquisition times has hindered its application in clinical routines and the combination of X-ray dark-field imaging and large field-of-view (FOV) tomography in the past. In this work, we propose a processing pipeline to address this issue in a human-sized clinical dark-field CT prototype. We present the corrective measures that are applied in the employed processing and reconstruction algorithms to mitigate the effects of vibrations and deformations of the interferometer gratings. This is achieved by identifying spatially and temporally variable vibrations in air reference scans. By translating the found correlations to the sample scan, we can identify and mitigate relevant fluctuation modes for scans with arbitrary sample sizes. This approach effectively eliminates the requirement for sample-free detector area, while still distinctly separating fluctuation and sample information. As a result, samples of arbitrary dimensions can be reconstructed without being affected by vibration artifacts. To demonstrate the viability of the technique for human-scale objects, we present reconstructions of an anthropomorphic thorax phantom.