Cardiac motion and partial volume effects (PVE) are two of the main causes of image degradation in cardiac PET. Motion generates artifacts and blurring while PVE lead to erroneous myocardial activity measurements. Newly available simultaneous PET-MR scanners offer new possibilities in cardiac imaging as MRI can assess wall contractility while collecting PET perfusion data. In this perspective, we develop a list-mode iterative reconstruction framework incorporating both tagged-MR derived non-rigid myocardial wall motion and position dependent detector point spread function (PSF) directly into the PET system matrix. In this manner, our algorithm performs both motion 'deblurring' and PSF deconvolution while reconstructing images with all available PET counts. The proposed methods are evaluated in a beating non-rigid cardiac phantom whose hot myocardial compartment contains small transmural and non-transmural cold defects. In order to accelerate imaging time, we investigate collecting full and half k-space tagged MR data to obtain tagged volumes that are registered using non-rigid B-spline registration to yield wall motion information. Our experimental results show that tagged-MR based motion correction yielded an improvement in defect/myocardium contrast recovery of 34-206% as compared to motion uncorrected studies. Likewise, lesion detectability improved by respectively 115-136% and 62-235% with MR-based motion compensation as compared to gating and no motion correction and made it possible to distinguish non-transmural from transmural defects, which has clinical significance given the inherent limitations of current single modality imaging in identifying the amount of residual ischemia. The incorporation of PSF modeling within the framework of MR-based motion compensation significantly improved defect/myocardium contrast recovery (5.1-8.5%, p < 0.01) and defect detectability (39-56%, p < 0.01). No statistical difference was found in PET contrast and lesion detectability based on motion fields obtained with half and full k-space tagged data.