Iterative tomographic reconstruction has been established as a viable alternative for data analysis in phase-sensitive x-ray imaging based on the edge-illumination principle. However, previously published approaches did not account for drifts of optical elements during a scan, which can lead to artefacts. Up to now, the strategy to reduce these artefacts was to acquire additional intermediate flat field images, which were used to correct the sinograms. Here, we expand the theoretical model to take these effects into account and demonstrate a significant reduction of (ring)-artefacts in the final reconstructions, while allowing for a significant reduction of scan time and dose. We further improve the model by including the capability to reconstruct combined absorption and phase contrast slices, which we experimentally demonstrate to deliver improved contrast to noise ratios compared to previously employed single shot approaches.