The decoupled power and energy output of a redox flow battery (RFB) offers a key advantage in long-duration energy storage, crucial for a successful energy transition. Iodide/iodine and hydrogen/water, owing to their fast reaction kinetics, benign nature, and high solubility, provide promising battery chemistry. However, H₂-I₂ RFBs suffer from low open circuit potentials, iodine crossover, and their multiphase nature. We demonstrate a H₂-I₂ operation with a combined neutral-pH catholyte (I₃^-/I^-) and an alkaline anolyte (KOH), producing an open circuit cell voltage of 1.28 V. Additionally, we incorporate a pressure-balanced gas diffusion electrode (GDE) to mitigate mass transport limitations at the anode. These improvements result in a maximum power density of 230 W/m² when allowing a mild breakthrough of H₂ through the GDE. While minimal crossover occurs, side reactions of permeating active species were found reversible, enabling long-term operation. Future work should address the stability of the GDE and optimization of the electrolyte thickness and concentration to fully leverage the potential unlocked by balancing the pressure and pH in the H₂-I₂ RFB.