I'd have figured the methane would be reformed to H2 first: nominally, H2O + CH4 -> CO + 3 H2 + H2O -> CO2 + 4H2 3H2 + FexOy -> H2O + Fe about 1.2-1.4x the me

I'd have figured the methane would be reformed to H2 first: nominally, H2O + CH4 -> CO + 3 H2 + H2O -> CO2 + 4H2 3H2 + FexOy -> H2O + Fe about 1.2-1.4x the methane winds up as CO2 (some extra is burned for heating in the reforming step). In this order H2 could be just as easily, but far more expensively, produced via green methods. Another green way would be to use aluminum to refine iron, Al + FexOy -> Fe + Al2O3. Exothermic, rapid, 'green', but expensive because it costs electricity to make Al. Also to your main point in modern blast furnaces I believe CO is either recycled or allowed to react with Fe2O3 at lower temperature to go all the way to CO2, saving money on coke: Fe2O3 + 3CO → 2Fe + 3CO2 or Fe2O3 + 3C -> 4Fe + 3CO2