Posted the follow-up for this thread......
My neighbor picked up a Tripp-Lite 2000W MSW inverter/charger and the optional remote panel.
We wired a 10' run of 2/0 wire from the house batteries (a pair of 200AH AGMs) to the inverter with a 200A Blue Sea circuit breaker in the positive lead at the batteries. We selected a 200A breaker since at full output the inverter will be drawing 166A at 12V (2000W).
The final wiring was somewhat different than what I posted above (what was I thinking??) and is shown here:
It was really quite simple as we just put the 110VAC pass-thru part of the inverter before the transfer switch.
We initially had a 200A fuse in the + lead instead of a circuit breaker, and when running the microwave (1800W input) the battery voltage would sag to around 11.4V. Looking at the giant 2/0 wire we ran, and seeing the tiny filament in the fuse prompted the switch to a circuit breaker. Now the voltage sags to around 12V when running the micro with fully charged batts.
Works fine so far...