Can someone review my plan - panels, controller, inverter, batteries - any input greatly appreciated

I would not consider a 3000 watt inverter on a 12 volt system. In fact when I wanted to run an air conditioner, I switched my system voltage to 24 volts. It really just not practical to run a large inverter off of a low voltage system. I am personally not a fan of running multiple system to serve the same building. Your well insulated I don't think you will have a lot of run time once you have cooled the place down. If your area cools at night and If that's your plan, to run mostly during the day, I think it's doable and reasonable. Running from stored energy will present some issues.

I also don't like multiple strings of batteries. You haven't spoken as to your storage. You won't be able to run the air conditioner without batteries. Since the array of 4 x 355= 1420 watts should be close to maxing out the Classic 150 at 12 volts, producing 90+ amps in bulk and 74 amps at absorb, the array would support a 600 -900amp hour battery bank, That would be 3 strings of golf cart batteries. I think you could run it without fear on 4 golf cart batteries, particularly when running a load during the day, but I might throttle them back during 'off season' for air conditioning.

I suspect you have read that there are NOT a lot of fans of Aims inverters. This is better than the last 3000 watt 12v Aims inverter I looked at which used 55 watts while on! I would suggest an inverter large enough to run the air conditioner, but small enough to run reasonable sized wire and less fear of voltage sag for the system if maxed out. Something like the Samlex PST 1500, it has the option of being hard wired. They make a cheaper one for around $365, but without this option.

https://www.solar-electric.com/samlex-pure-sine-wave-inverter-pst-1500-12.html

I would think you would be a little undersized array to load, but time will tell.

I ran a similarly sized array in my tiny cabin. 10 x 16 also with roughly R21 walls. I had 4 - 1 year old golf cart batteries from a earlier system and it was enough to keep me cool for sleeping in Missouri, where our nights tend to cool off. But I was 'push n' pull'ing the batteries pretty hard. Usually taking them down to 50% SOC(or less) every night. They hung in there for 5 years/4 summers. They were setup in a 24 volt bank and I was using a PWM charge controller. My cabin was in the shade as well.

I don't know if you will be able to run the AC around the clock, even with 2 strings of golf cart batteries. I would set it on timer to turn it's self off after 3-4 hours and turn it back on when the sun hit the array fully. You should be able to run the AC and charge the batteries, particularly if you find the duty cycle (time the compressor runs) to be 50% or less.

I miss my cabin, no chance of moving it, it was 14 feet tall;

I'll concur with moving to a 24v system with your panels, and using only four Golf Cart batteries (6v 200ah) wired in series The batteries buffer the solar fluctuations, but late afternoon as the sun angle changes, you will have to shut down.

Inverter size, as small as you can, while still being able to start the AC. A 2Kw inverter with good 2/O battery cables, should do it,