If you have sized a fuse for 350 amps, you really need to consider going to a higher voltage system. Start looking at the amps city of wire, When I checked, 4/0 goes to 260 amps. THat’s pretty thick wire to work with.
I am not a fan of 3000 watt inverters on 12 volt systems Because of how thick the wire needs to be, FOr systems that really gets used, 12 volts is good to 1000 watts, except for a four or five excursions a day to 2000 watts to power a microwave a couple minutes at a time. Many will disagree with that.