This paper demonstrates a robust diffusion-weighted single-shot fast spin echo (SS-FSE) sequence in the presence of significant off-resonance, which includes a variable-density acquisition and a self-calibrated reconstruction as improvements. A non-Carr-Purcell-Meiboom-Gill (nCPMG) SS-FSE acquisition stabilizes both the main and parasitic echo families for each echo. This preserves both the in-phase and quadrature components of the magnetization throughout the echo train. However, nCPMG SS-FSE also promotes aliasing of the quadrature component, which complicates reconstruction. A new acquisition and reconstruction approach is presented here, where the field-of-view is effectively doubled, but a partial k-space and variable density sampling is used to improve scan efficiency. The technique is presented in phantom scans to validate SNR and robustness against rapidly varying object phase. In vivo healthy volunteer examples and the clinical cases are demonstrated in abdominal imaging. This new approach provides comparable SNR to previous nCPMG acquisition techniques as well as providing more uniform apparent diffusion coefficient maps in phantom scans. In vivo scans suggest that this method is more robust against motion than previous approaches. The proposed reconstruction is an improvement to the nCPMG sequence as it is auto-calibrating and is justified to accurately treat the signal model for the nCPMG SS-FSE sequence.