Thanks for your time, Chris.
It's technically a 1000 watt inverter (typo in diagram), with 2200 peak. My gut was to go with 2|0 with a 200 amp fuse, but thought that might be overkill?
The 100 amp battery fuses is for the wire, since 4 AWG is rated for 100 amps. I doubt I will be pulling that...