You also need to take into account the instant discharge current of your batteries, using the rule of thumb of 10 amps per 100 watts, a 1200w coffee machine would draw 120 amps (albeit for only a few seconds). Your batteries would need to have a combined discharge current of 120 ampsI know it's an old thread but interested to hear how you got on?
I got a mini nespresso, 1500w pure sine wave inverter and 200ah AGM batteries and still can't use it without the engine running...? I used 170a 25mm2 cable to be sure it could cope but still no dice. Battery limitation maybe?