@Nemiyen The problem that I see is for example, the suns shining brightly, 4kw is being generated, the system turns on 2 x 2kw heaters, the sun goes behind a cloud, and is now generating 1.25kw, what happens??? The piddling small battery is flat, and there's no grid, do you get horrendous voltage drop, which increase current, or does the inverter just trip off?
As
@HungryHippos said, just do a grid connected system, believe me it gets very complicated very quickly even doing something slightly different to the norm let alone what you're proposing.