Diffusion MRI (dMRI) offers a unique probe into neural connectivity in the developing brain. However, analysis of neonatal brain imaging data is complicated by inevitable subject motion. Here, we develop a method for reconstructing multi-shell HARDI data from scattered slices, jointly estimating an uncorrupted data representation and per-excitation (slice or multiband package) motion parameters. The reconstruction relies on orthogonal decomposition of multi-shell dMRI data using a bespoke spherical harmonics and radial decomposition (SHARD), together with outlier rejection, distortion, and slice profile correction. We evaluate the method on publicly-released datasets for 40 neonatal subjects from the developing Human Connectome Project.