I'd attribute that to your batteries, not voltage loss in the cables. Called Voltage sag. How big (capacity) is your battery bank? I have a decent 560Ah LiFePO4 battery bank. It will run an AC unit for quite a few hours.Wondering if you're willing to share any data. I've got a SAMLEX 2000 watt Pure Sine Wave hooked up with 4/0. I got this to run 1200 watts for three to five minutes, microwave popcorn. I have not done that, but I had the inverter running for a few minutes at 1100 watts output and I measured the temps, and the wires never warmed up, and neither did the inverter. I was pretty happy with that. With the solar panels running, the voltage never dropped, but at night time, voltage draw went from 12.6 to 12.0.
Doug