42c! damn that's hot. The concern with inverter inefficiency isn't so much whether it can handle high temperatures and keep a fridge cool, its the extra wasted power that you have to account for. Though the ability to keep frozen things frozen and cold things cold is pretty important too, especially the former.
This is important, other than efficiency, its the other main concern I have with a normal household mini fridge. But if yours can handle 1000's of K's of corrugation, it should handle most anything you come across. What brand? edit: just reread your previous post and saw it is a Samsung 220v
How are you defining/measuring efficiency here? Lower power draw at a given temperature including inverter overhead? Lower power draw of the fridge only? More effective at freezing things? All of the above?
Most proponents of AC fridges don't claim that they are equal or more efficient. The argument is usually that the marginally better efficiency of 12/24v units doesn't justify the added cost. And it is a persuasive argument for many use-cases. But I haven't heard anyone claim their 120/220 AC unit was more efficient (since the fridge itself is DC and requires a conversion from DC (batteries) to AC (inverter to wall plug) and then back to DC (fridge internals) with associated efficiency losses at each conversion poitn, it seems it would be impossible to be more efficient if all other things are equal. Maybe your 220v fridges in Australia are made to a much higher energy efficiency standard than here in the US (I think this is true in the EU) but I still have a hard time believing your 220v unit can be more efficient than a DC fridge in a DC system unless I'm fundamentally misunderstanding something (which is likely ?).
This is probably a big part of the reason you don't care about inverter inefficiency or fridge inefficiency. 400ah is a lot more than most offroad builds have. If a fridge is a small part of your total energy budget saving 10-30% doesn't matter much, if its your main energy consumer and you only have 1200w/hrs as is common in small builds, 10-30% savings can be huge.
I don't understand why having a generator or charging from alternator would affect your decision to go with a 12v fridge or not? regardless of whether you use 12v or 220v your system is 12v, your drawing power from your batteries and charging from the sun. What am I not understanding?