A similarity-driven multi-dimensional binning algorithm (SIMBA) reconstruction of free-running cardiac magnetic resonance imaging data was previously proposed. While very efficient and fast, the original SIMBA focused only on the reconstruction of a single motion-consistent cluster, discarding the remaining data acquired. However, the redundant data clustered by similarity may be exploited to further improve image quality. In this work, we propose a novel compressed sensing (CS) reconstruction that performs an effective regularization over the clustering dimension, thanks to the integration of inter-cluster motion compensation (XD-MC-SIMBA). This reconstruction was applied to free-running ferumoxytol-enhanced datasets from 24 patients with congenital heart disease, and compared to the original SIMBA, the same XD-MC-SIMBA reconstruction but without motion compensation (XD-SIMBA), and a 5D motion-resolved CS reconstruction using the free-running framework (FRF). The resulting images were compared in terms of lung-liver and blood-myocardium sharpness, blood-myocardium contrast ratio, and visible length and sharpness of the coronary arteries. Moreover, an automated image quality score (IQS) was assigned using a pretrained deep neural network. The lung-liver sharpness and blood-myocardium sharpness were significantly higher in XD-MC-SIMBA and FRF. Consistent with these findings, the IQS analysis revealed that image quality for XD-MC-SIMBA was improved in 18 of 24 cases, compared to SIMBA. We successfully tested the hypothesis that multiple motion-consistent SIMBA clusters can be exploited to improve the quality of ferumoxytol-enhanced cardiac MRI when inter-cluster motion-compensation is integrated as part of a CS reconstruction.