FeCoNiCu(Cr, Mn, La, Ce)-Al high-entropy alloys (HEAs) were prepared via a combined centrifugal casting–self-propagating high-temperature synthesis process to serve as multifunctional catalyst precursors. The findings indicated that even with aluminum content reaching 50 wt %, the typical bcc structure inherent to HEAs was preserved. Doping additions (Cr, Mn, La, and Ce) led to pronounced microstructural changes, including alterations in morphology, porosity, and elemental distribution, while the primary phase constituents of the FeCoNiCuAl-based alloys remained consistent. It was found that La and Ce exhibited poor bulk incorporation into the HEAs, evidenced by a low surface content. Aluminum leaching and hydrogen peroxide stabilization converted these precursors into catalysts. These catalysts demonstrated high activity in the deep oxidation of propane and CO. The FeCoNiCu catalyst achieved the best results for CO oxidation, reaching 100% CO conversion at 250 °C. For propane oxidation, the FeCoNiCuCrMn catalyst was the most active, yielding 100% CO conversion at 300 °C and 97% propane conversion at 400 °C.