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Compared to standard tomographic reconstruction, iterative approaches offer the possibility to account for extraneous experimental influences, which allows for a suppression of related artifacts. However, the inclusion of corresponding parameters in the iterative forward model typically leads to longer computation times. Here, we demonstrate experimentally for phase sensitive X-ray imaging based on the edge illumination principle that inadequately sampled illumination curves result in ring artifacts in tomographic reconstructions. We take advantage of appropriately sampled illumination curves instead, which enables us to eliminate the corresponding parameter from the forward model and substantially increase computational speed. In addition, we demonstrate a 30\% improvement in spatial resolution of the iterative approach compared with the standard non-iterative single shot approach. Further, we report on several significant improvements in our numerical implementation of the iterative approach, which we make available online with this publication. Finally, we show that the combination of both experimental and algorithmic advancement lead to a total speed increase by one order of magnitude and an improved contrast to noise ratio in the reconstructions.