Thank you for your very detailed post. It makes the subject much clearer!I know this thread is dead, but I wanted to explain something for if anyone else comes along and reads it.
A sine wave inverter wattage is measured at the output. This means that a 1500w sinewave inverter, if running a 240V(in Australia) output would allow for 6.25A. Also, a pod coffee machine that runs at 1350-1450W pulls (1350/240=5.62) 5.62A-6.04A. You are all calculating wattage off the 12V DC voltage, which is extremely inaccurate.
If you don't believe me, think of a pod machine plugged into the wall at home. Nothing has changed with the pod machine, it still around off 240 and still pulls the same power. If it does that, at 160A or so, how can the wire from the wall to the machine be such a small cable?
Some pod machines, such as nespresso, have a microprocessor inside them that detects an unregulated power source and prevents too high of a current drawer to prevent cooking it by accident. But if you get a lower cost machine, such as an ALDI one, it should work fine. A deep cycle 100Ah battery will run one of them (if it's pulling water the whole time), in theory, or 20 hours before killing the battery.
Bare in mind, some inverters are different to others and you can't exactly calculate the power draw on the 12V side, but it wouldn't be 160A. If you want to know how much you are drawing, turn the machine on and feel how hot the cable gets, for every 20 degree increase in temp you are drawing double the amount of power. No hot = no low battery.