I'm not sure where you will tie it "into the system," but I will point out that this is a 30A+ load. That's a LOT of current, especially for any load near capacity for any length of time (I don't see it as a battery issue -- I know you won't run a 400W load on battery for more than a few moments -- it's more of a circuitry thing). That kind of load needs to have short wires to keep losses to a minimum. I would suggest perhaps tying right off the battery switch.That's an explanation that makes sense. Now that I'm done testing the inverter to see if it works, I will hard-wire it into the system. Should I put it on its own breakered circuit, or use an inline fuse?
As far as a breaker or an inline fuse, the first issue is size -- can you get an inline fuse big enough? If you can, the on-off switch on the unit is probably suitable for the control of power, and the fuse is suitable for protection. If you ever need to take the circuit down hard, you can just pull the fuse.
Harry