So this is what I ended up doing. I think it worked out alright.
Fuse inside 5" square box. About 14" of lead wire (unfused) and 5 ft of wire to the inverter.
This is the inverter I bought. Installed inside the cubby where the water heater and pump are.
These are the inverter switch and lower left receptacle is inverter power and the one above was existing 120v. I had the TV on for 30 minutes in 28C weather and the inverter fan didn't kick on. Not even warm to the touch.
I'm happy with the way it worked out and really happy I installed the box to contain the 100amp fuse. It didn't feel right the first way I had it installed. Thanks for the advice!