Well I finally got this work done. Here is what I ended up doing....
Mounting the Inverter: I mounted the inverter on its side under the rear seat, parallel to the charger. One bolt holds it to the rear seat metal base frame, but I didn't have room to get my drill down near the floor to make holes for any other bolts, even with the charger removed. So, instead, I used L-brackets screwed to the floor to hold the inverter in place. I put some foam on the floor to hold the inverter up off the floor, so the sharp edge of the inverter's metal case wouldn't dig into the soft wood and plastic underneath.
Inverter Input Ground Connection: My van's ground terminal block has four screw connections, of which two were populated by thin-gauge wire, so I combined those two into one -- freeing a connection for the inverter's ground (rightmost in the photo).
Inverter Input +12v Connection: Here is the 150A fuse I used for the inverter's 12v positive input. I then wired from the fuse to the "house battery" connection on the separator (left connection in photo).
Inverter Output to Outlets: The outlets on my van used to be wired into the external "shore power" via a GFCI outlet mounted externally under the rear seat. I removed this GFCI outlet, replacing it with the non-GFCI outlet that used to be mounted hidden away under the rear seat and used for the charger's input. This externally facing outlet is now powered by my new inverter, and connects to all the other outlets in the van. To power the outlet with the inverter, I connected it using a beefy power cord. I cut the female end off this power cord, and wired it into the outlet. Unfortunately, the power cord used stranded wire, which wouldn't stay put inside the outlet the way it's designed. I ended up soaking the wire strands in solder, and this made them behave like solid core -- properly seating themselves in the outlet. The male end of this power cord then plugs into the GFCI outlet of my new inverter.
Charger: The charger has a power cord that wants to be plugged into external "shore power". Rather than building an outlet box just for this purpose, I again used a power cord. I cut off the male end of this power cord, and wired it into the fuse box. Then the charger's power cord plugs into the female end of my cord so it can be powered from the fuse box.
Inverter Remote Switch: I mounted this under my sink. There was a vacant space just the right size for this remote switch!
Here is what the whole mess looks like in the end. I later wrapped all wires with corrugated split loom for protection against rubbing when the van shakes on washboard roads (not pictured).
--Geoff