With increasing appreciation for the extent and importance of intratumor heterogeneity, much attention in cancer research has focused on profiling heterogeneity on a single patient level. Although true single-cell genomic technologies are rapidly improving, they remain too noisy and costly at present for population-level studies. Bulk sequencing remains the standard for population-scale tumor genomics, creating a need for computational tools to separate contributions of multiple tumor clones and assorted stromal and infiltrating cell populations to pooled genomic data. All such methods are limited to coarse approximations of only a few cell subpopulations, however. In prior work, we demonstrated the feasibility of improving cell type deconvolution by taking advantage of substructure in genomic mixtures via a strategy called simplicial complex unmixing. We improve on past work by introducing enhancements to automate learning of substructured genomic mixtures, with specific emphasis on genome-wide copy number variation (CNV) data, as well as the ability to process quantitative RNA expression data, and heterogeneous combinations of RNA and CNV data. We introduce methods for dimensionality estimation to better decompose mixture model substructure; fuzzy clustering to better identify substructure in sparse, noisy data; and automated model inference methods for other key model parameters. We further demonstrate their effectiveness in identifying mixture substructure in true breast cancer CNV data from the Cancer Genome Atlas (TCGA). Source code is available at https://github.com/tedroman/WSCUnmix.