Well, IMO the cyclic starting surge of the reefer will be a big hit on the RL system even when engine running. Most backup schemes using battery>inverter are based on deep-cycle batteries, different from car-starting batteries in their design behavior characteristics.
Personally, if I lived in a place where Edison was pulling this sort of stunt on a more-or-less ongoing basis I'd be shopping for a compact portable 1-2KW gasoline inverter / generator. They can be had for not terribly much more than a quality 1500W bare battery-based inverter, are actually designed for that sort of duty, can serve more capably and economically than running your RL, serve other useful benefit beyond just the reefer, etc, etc.
The Honda EU2000 is the top-of-the-line most expensive option of that sort but there are now several
much less expensive and reasonably reliable alternatives on the market, google is your friend.
It was my understanding that a capacity of 500-600 AH was not uncommon for car batteries. Maybe I misremember.
That's big numbers for Amp Hour 'capacity' ratings, more like Cold Cranking Amp numbers (there's a world of difference between Amp
Hours and CC
Amp ratings). Remember that most car battery specs for 'reserve capacity' are an expression of "minutes" at a standardized load condition, not Amp Hours. Methinks you're mis-remembering values and/or confounding different battery spec measurements / units.
