Itinerant1,
What a WONDERFUL report. ty so much.
My bank was originally 875 amp-hours of Marine jars. This was chosen because I knew I wanted to run the block heater for 3 hours during temperatures in the -30 to -40 range.
Four years ago I moved to used telecom batteries--556 amp-hours. The Marines were 11 years old and I simply got tired of laying down in the snow to check electrolyte levels.
My solar does, best case, about 17 amps @ 12 volts (nominal). I'm sure the voltage sag on LI is not as great, but equally your solar farm is much larger than mine.
My air conditioner doesn't stumble--but the red light on the Magnum remote does raise its ugly head on the air conditioner starting from scratch when on the generator (eco on), or on just the inverter.
One interesting side bit of information. If the battery bank is depleted, with load support on, and input amps limited to 12 (on a 15 amp shore power connection), then that "limit" will be overridden, and the shore power breaker at the pedestal will trip if you exceed the rating on the breaker.
That happened when I was having the RV cleaned. My cleaner has me park the RV in front of her home. It was winter and I was running electric heaters. She plugged in the vacuum, and that was enough to cause the trip. Her husband reacted quite badly. You would have thought I had caused a whole subdivision to loose power.