AC/DC inverter current readings

Your ammeter(s) is (are) lying? Odd waveforms will fool most ammeters. For the AC side, buy a "KilloWatt" or one of its clones. For $25 it's a good investment for the curious. I'll show true RMS voltage, current, power, VA, PF, Hz, kWh, and pretty much anything else you want to know. Mine has the Seasonic logo on it.

Your AC ammeter isn't reading things properly. Most cheaper AC ammeters make the assumption that the waveform it's receiving is a pure sine wave, and measure based on that assumption. Your inverter generates something marketing calls a "step sign" which in reality is just a thee value "square" wave (+V, 0V and -V). Cheaper meters will be grossly wrong in reading the RMS current of such a waveform.

You need an AC ammeter that calculates the TRUE RMS value. Look for any ammeter from a brand name company that mentions "True RMS".

TTYL

I think possibly you mean "step sine"?

Although that is normally used to describe something with at least one intermediate value on the way up and down..

Yes, typo on my part. I personally have a BIG problem with them calling it a "step sine" since it makes people who don't know much think it's a sine wave. I once showed the "step sine" waveform to a friend of mine and he couldn't believe that's what the inverter was generating, he thought it generated a slightly "jaggy" sine wave (a sine wave made out of very small discrete steps).

While the term may technically be at least partially valid, I find the confusion it generates cause enough to get the term banned.

I always say, marketing is the art of lying, and getting away with it.

Just my opinion.

TTYL

A possibility not mentioned is that your ice box draws a fair amount of "reactive power." The DC reading times the input voltage (12?) is definitely the power input. On the output side you need a proper wattmeter to measure power. AC amps X AC volts gives you a higher power than actually consumed.

The comments about the waveforms not being sine waves are also valid.