or you can maybe skip the hydrogen intermediary on one end and burn the iron in an iron-air battery. then you get much higher efficiency. electrowinning of iron in alkali is also feasible, eliminating the hydrogen on both ends
well, adding iron and removing iron oxide is what electrowinning iron does, but i think i added that part of my comment after you made yours. but you can still add iron and remove iron oxide with the hydrogen smelting furnace the ethz researchers devised if you like that better