I agree with RickLight. The circuit is a circle. If ANY part requires 4/0 cable, the battery negative NEEDS to also be 4/0 cable.
If the inverter requires 4/0 cable, then the complete pathway back to the battery terminals need to be 4/0 cable. Either that, or wire the inverter directly to the battery rather than to the buss.
My Airstream got around having to use large cable for the trailer by wiring my inverter directly to the battery. (That meant I had to install a separate disconnect relay just for the inverter.)