John... you are correct in that the PI or Watchdog will reset after a period of time. The voltage will have to come up to a normal range before the reset can take place. It can be a few minutes or a few hours. During that time your refrigerator is either on LP or in my case house batteries.
In my understanding, the autoformer never lets the event happen to you. It uses a transformer to constantly adjust the voltage to "Normal" so it never goes low and shuts down.
They are very common in industrial machinery that is designed for 240V but the commercial power is only 208V. I have several on machines to raise the voltage. Heating elements (inductive load) become very inefficient when the voltage is low. A heater may come up to temp in 5 minutes at 240V, but takes an hour at 208V.
So my thought was the Autoformer first and the Watchdog second and then into the transfer switch. It's only my opinion... having owned an RV for exactly 1 day.
Paul, Emily & Darla Mae (JRT)
2021 Tiffin RED 37BA
2019 Jeep Wrangler Sport 2 Dr