I have seen several people run off of batteries and actually doing the batteries then generator then back to batteries is the most efficient way of getting the most out of your fuel usage and generator life.
The biggest system I have ever seen was a guy I sold 96 4 volt 300 Ah batteries too.
(I ran his bank out of $100 bills when I cashed the check too!)
His system was 24 volt and originally ran on 12 6 volt 200 Ah golf cart batteries connected as a series/ parallel. Four batteries in series to get 24 volts and then three sets like that in parallel. The total capacity was 24 volts 600 Ah.
Each set of four batteries had a 100 amp fuse so if one bank went bad it just blew that fuse and let the other two sets still run.
His home electrical system was similar to what your talking about. He had one smaller sized modified sine wave inverter that covered all the lighting duty and was always on. A second unit was dedicated to the well pump and some of the higher load devices in the shop. That one cycled on as needed.
There was a third one that ran the kitchen stuff and also was set up to cycle at certain times of day or could be manually ran also, I think.
I dont see why your entire system could not be set up similar. I would however set up the battery bank as a set of 9 series parallel units with a 50 -100 amp fuse or breaker for search set. That way your total amp draw per battery is low and thus the discharge time rate will be at its most efficient.
However, charging a 12 volt 2880 Ah (30+ KWh usable) battery bank will take a fair sized generator and battery charger! Factoring in recharge efficiency losses you would need a charging system that could supply at least 4 kw at 14.4 volts (280 amps) for around 10 hours if the batteries are run down.
But over all your system has great potential and if properly done It should be easy to work with and maintain. Plus adding solar or wind or alternative fuel charging systems is not hard.
A propane powered gen set is far cheaper to run and lasts far longer than a gasoline powered one too.
For the high amp low voltage charging using 4 to 6 100 amp alternators run off a small car engine at low RPM, 900 - 1200 RPM engine speed with a 4:1 belt speed increase at the alternators, will save you fuel and get an incredible running life if propane powered.
I have seen two rigs set up that way before and both owners said they were far more fuel efficient than a small engine and the expected running life was in the 10's of thousands of hours!
Plus both used the engine and exhaust heat to make hot water for heating their homes and hot water heaters. That makes the fuel use during charging cycles even more efficient when the engine waste heat is captured and used in a positive and constructive way.
The set up cost and time involved will be more to do it this way but the added gains will make the long term use far more cost effective.
Just somethings to think about.