You can't escape the cable requirements.
Even at 50mm between your battery and your 3kva inverter you still need a 240amp cable which will be 75mm2.
You could derate your inverter by installing a switch board with 10amp breakers, but this will drive your cost up fast as it requires an electrician and a inverter that can have a MEN configuration. Most inverters used in 12v cheap installations are IT, they have the plug/socket on them and you shouldn't run multiple devices off a single plug.
I am yet to find a 12v LFP battery on the NZ market that is rated for 1C discharge. Most