The experimental realization of new functional materials is a complex optimization problem that would vastly benefit from the application of high-throughput methodologies. In this work, we adapt bulk ceramic processing for high-throughput integration, with a focus on producing high-quality thermoelectric materials. We also monitor the time and effort cost per sample, providing insight for where additional engineering can further increase throughput. Through parallelization and automation, we achieve a 5-10x increase in synthetic speed, allowing the generation of a 121 sample alloy map within the PbTe-PbSe-SnTe-SnSe system. Despite heavy investment from the thermoelectric community, prior literature exclusively focuses on intuitive pseudobinary combinations within the PbTe-PbSe-SnTe-SnSe alloys. Our intuition-agnostic mapping, however, has enabled us to identify compositions with anomalous, non-monotonic changes in the thermoelectric transport. The newly discovered trends (e.g. high mobility alloys, extended band-inversion region) do not lie on the intuitive pseudobinary combinations - exemplifying the value of unbiased high-throughput methods. Additionally, as our methods were chosen explicitly to preserve sample quality, our solubility limits and room-temperature thermoelectric transport are also in excellent agreement with available literature. Ultimately, this work demonstrates that high-throughput methods are a potent tool for the accelerated optimization and realization of new functional materials.