OK, well, my thoughts would still be on reducing useage if possible - though without knowing anything about running a poultry business I don't have a handle on what is possible.
As for timers - well you can get electronic ones with battery backup for central heating at least, which would solve that problem with a.c. shutdown.
But, getting back to the original question of considering the system you have been offered:
Obviously I don't know what the system's going to cost vs running the generator, but one question I would be asking would be regarding the cost & life expectancy of the battery:
Is it a lead acid traction (forklift) battery or a modern Liion?
Is the 20kwh rating refer to 100% nominal depth of discharge (DOD) or to 80%? 50%?. The life of a battery depends on the type and how deeply you discharge it. with lead acid, even 'deep cycle' traction batteries don't like being drained beyond 80%DOD, and even if your stopping at 80%, doing that daily will mean you will be buying a new battery fairly often.
Liion are better at tolerating 80-100% DOD but still last a lot longer if you keep them on shallower cycles, and are a lot more £££ than the lead acid.
As a smaler scale alternative I might think about using the 4kw (or even a bit more) solar via a grid-tie inverter direct to the generator as it would reduce loading during the day, and if it's a GTI which 'backs off' when the ac frequency rises above 50Hz, then in the event that the solar output exceeded consumption, the solar GTI output would automatically reduce once it started to 'push' the generator overspeed (in theory).