What an honest assessment?
I think you have got about a snowball's chance.
Yes, if it the right number Dometic, it might not be too bad.
You don't know how much you will use the water pump, and unless go to bed and get up with the sun and even with LED in all the lights, there is not a real good chance that you will make three days on a single Grp 27 conventional. That size jar is typically 90Ah (Ampere-Hours), and you get to use only the top half without damaging the battery.
Are you aware that recovering a conventional battery from 90 to 100% State of charge will take ~4 hours unless you want to risk all you DC equipment with a higher charge voltage, Then you can make it 3 hours. But, you can get from 80% to 90% in an hour it you have the right stuff in place.
My best bet?
Make a plan. Run you generator either 2 hours every day or 4 hours every other day. Or, just watch the voltmeter. When it gets close to 12.2, start the APU(genset). That way, the house bank is never that far gone, but you also don't get to count on it being 100%.
Matt