As others have said there is a lot of unknowns but I can tell you of my experience. I have a 2016 Miramar with an 1800 watt inverter and had 2-6 volt deep cycle batteries. I would turn the generator off at 10:00 pm and the low battery warning would begin beeping at 5:00 am.
I had the AutoGenStart set to not run from 10:00 pm to 7:00 am so I couldn't make it through the night. I replaced the 2 batteries that came with the coach with 4-6 volt 235AH batteries. I haven't had a problem since.
You could also shut off the fridge just before going to bed and it should remain cold enough through the night. A couple hours of running the generator should bring the batteries back to normal.
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