State-of-the-art manufacturability evaluation of sheet metal components, particularly drawability assessment, relies on high-fidelity explicit finite element (FE) simulations. While FE simulations can accurately predict material behavior during forming, they are computationally expensive and therefore ill-suited for use in early design stages. Recent advances in supervised machine learning (ML) have demonstrated strong potential for data-driven drawability prediction, enabling rapid design evaluation. However, existing ML models remain challenged by inter-part-class prediction, where training samples originate from heterogeneous sources (e.g., company-internal vs. public datasets, parametric vs. non-parametric geometries, etc.). In such settings, achieving industry-level prediction accuracy typically requires large labeled datasets, which are scarce in sheet metal forming applications. Several strategies exist for generating additional training data, including parametric variation, generative ML approaches, and geometry-based augmentation techniques such as scaling, filleting, or slicing. However, these methods do not inherently provide drawability labels and therefore still require additional FE simulations. Moreover, they do not guarantee improved coverage of the underlying non-parametric, geometry-driven design space and may generate samples outside the initial design domain. Insufficient design space coverage is particularly detrimental to generalizability in inter-part-class prediction scenarios. In this work, we present a geometry-driven framework for design-space-aware data augmentation based on uniform scaling-invariant higher-order geometric moments to quantify geometric similarity between sheet metal parts. Pairwise distances in moment space are embedded using multidimensional scaling, yielding a low-dimensional representation of the non-parametric inter-part-class design space. Sparsely populated regions and coverage gaps in this space are identified and used as optimization targets to guide geometric data augmentation toward underrepresented areas. In contrast to existing augmentation strategies, the proposed approach explicitly incorporates design space coverage as an objective, thereby reducing redundant samples and enabling more data-efficient label acquisition by limiting FE simulations to geometries that meaningfully expand the design space.