Casey, I hope you find this helpful. It would simplify what you have and I think it will be safer and more reliable.
You have other (smaller) wires going to your busbars as well. I have no idea what they are for but they can also go to the busbars in the drawing as long as they are fused.
You don't really have enough battery or solar to effectively run your A/C, so as long as you aren't running some high amperage appliance that I don't know about, singe 2/0 cable should be sufficient up to 200A+ at a 10' run.
By the way, I realize that you have a 3,000W inverter. That doesn't mean that you must run 4/0 wires if you never run anything over 2000W constant. 3000W is just what the inverter is capable of. That is not what you will running it at, unless you know something that you haven't told us. Even if you did run 3000W for a short time, you'd probably be OK with 2/0 pure copper wire.
You might like these 250A, protected busbars (they're also available in 350A):
https://www.amazon.com/Seamaka-250A-...1zcF9hdGY&th=1
These solar circuit breakers are a good ide too. They allow you to turn off the solar panel input so that you can work on your other components without risk of damaging your solar controller.
https://www.amazon.com/Miniature-Cir...s%2C156&sr=8-5