Proton ceramic reactors offer efficient extraction of hydrogen from ammonia, methane, and biogas by coupling endothermic reforming reactions with heat from electrochemical gas separation and compression. Preserving this efficiency in scale-up from cell to stack level poses challenges to the distribution of heat and gas flows and electric current throughout a robust functional design. Here, we demonstrate a 36-cell well-balanced reactor stack enabled by a new interconnect that achieves complete conversion of methane with more than 99% recovery to pressurized hydrogen, leaving a concentrated stream of carbon dioxide. Comparable cell performance was also achieved with ammonia, and the operation was confirmed at pressures exceeding 140 bars. The stacking of proton ceramic reactors into practical thermo-electrochemical devices demonstrates their potential in efficient hydrogen production.