I have read all of the posts and the attached article and all of them are good and are basically saying the same thing... except for the one from the retired electrician saying that only the battery the inverter is wired to will provide power of batteries wired in parallel. I think that was a joke.
The article was good, but it was flawed in that the differences it reported of current sourced from each battery is insignificant considering that the batteries wired in parallel with heavy gauge wires are always going to self equalize within minutes.
I always use water analogy to explain this to non-electrical trained people...
Volume/flow of water is electrical current. (gallons/minute vs amps)
Water pressure is voltage (PSI vs volts)
Pipe/opening size is wire resistance. (CV vs ohms) CV is technical flow coefficient term that considers pipe/opening size.
If you have 4 buckets with pipes/openings between them at the bottom of the buckets then the water level in each bucket is going to be exactly the same. If you pull lots of water out of a bucket (draw current load), then the water from the other buckets will flow into that bucket and in a very short time all the buckets will be at the same water level again but a lower level than before (battery charge level). The bigger the size of the pipe/opening (wire size) between the buckets, the faster this leveling occurs.
If you add water to a bucket (charging battery), then the water will flow into the other buckets and they will all be at the same level very quickly.
Now to the point I was trying to make.
Drawing over 100 Amps from your batteries through a large inverter is only a very short term solution and has a tremendous toll on your battery charge level that takes many hours to recover.
If you have high load AC power requirements it is always better to just crank up the generator for 10 or 15 minutes to provide the AC power for 1000W to 2000W loads and save your batteries for when you can't run your generator.
It really doesn't make sense to run 2000W load on your inverter for 10 minutes and then have to run your generator for 3 hours to recover your batteries or solar for +4 hour with full sun.
But this is a situational decision. If you want your Keurig coffee or toast at 6AM before you can run your generator due to noise to your neighbors, then yeah... use your inverter and then charge up your batteries for 2-4 hours of full sun or when you can run your generator. But if running the generator is an option, then it is by far the most efficient way to use your power sources.
I have only been on this forum for a short while and it is clear that there are many schools of thought on wire sizes. Yes bigger is better, but there is an economy of scale and laws of diminishing returns that should be considered.
I just found this link that is pretty good with reasonable wire size recommendations.
Running 4/0 wire is very expensive, is is huge and is very hard to route (you need to be superman to bend the wires). It requires a special crimping tool that is basically a large punch and a hammer. And going to 4/0 gets you from a 97% efficient solution with 1/0 to a 99.5% efficient solution that you will never see any real benefit from. Actually the connection termination point resistances dominate the current flow paths. They should be clean with good metal to metal (copper) surface area contact, great crimps and as tight as you can get them. (And they do come loose over time from vibration)