Ultra-low-field (0.064T) magnetic resonance imaging (MRI) systems enable portable brain imaging but pose significant challenges for automated segmentation due to low signal-to-noise ratio and limited resolution. We present a coordinate transform-based deep learning approach for pediatric brain structure segmentation that analytically handles geometric variability through spherical and ellipsoidal coordinate mappings. Our method employs an ensemble of SwinUNETR models trained in Cartesian, spherical, and ellipsoidal spaces, combined with two novel loss functions: Projection Dice Loss for shape-aware supervision through 2D orthogonal projections, and Coordinate-Aware Soft Hausdorff Loss using coordinate-appropriate distance metrics. Evaluated on the LISA25 challenge dataset, our ensemble achieved competitive performance with Dice coefficients of 0.72±0.17 for hippocampus and 0.85±0.05 for basal ganglia segmentation. While coordinate transformations provide principled geometric handling, inverse transformation artifacts limited their individual effectiveness. The novel loss functions demonstrate clear benefits for medical image segmentation, advancing automated analysis capabilities for portable brain MRI systems in resource-constrained environments. Source code is available at https://github.com/mahbodez/LISA25-public .