When treatment planning in ion beam therapy is performed based on X-ray CT data, the Hounsfield Units (HU) are approximately converted to relative stopping power (RSP). The range uncertainties associated with the conversion process require additional safety margins around the contoured treatment volume. Meanwhile, proton imaging provides a direct probe of RSP. A patient specific optimization of the HU- RSP conversion curve by comparing proton radiographic images with digitally reconstructed radiographies (DRR) has previously been suggested. In this contribution, we investigate the influence of several factors on the accuracy of this optimization, i.e., the projection model for the DRR, the co-registration of proton radiography and X-ray CT, and the choice of approximation intervals of the HU- RSP curve. For this purpose, experimental proton imaging data is inadequate because the true RSP values are not known for anthropomorphic phantoms of realistic complexity. Instead, we generate ground truth data through experimentally validated Monte Carlo (MC) simulations. To assess the expected therapeutical gain and the influence of the aforementioned factors thereon, we (re-)calculate treatment plans based on optimized and non-optimized X-ray CT (in RSP). We compare the predicted dose maps with the one obtained from a MC simulation of the treatment, with a special regard to edges near organs at risk. We will finally quantify by how much range accuracy can be improved through patient specific optimization of the HU-RSP conversion curve.