There seems to be an error in your calculation: Up to the 11 000 000 kgm required it is correct. However the Toyota Camry with 7.3 m provides only 11 000 kgm. So you miss a factor of 1000. You would need 1000 cars lifted the height of your home. For just one day (or a few days in more efficient home)
What you describe is more like black start, providing power to the grind when it is down. This has to be controlled well, and only a few plants need to be capable of it.
Grid following means something like whatever the grid does, the inverter injects power supporting it. A grid forming generator or inverter also follows the grid somewhat, but tries to get it to an optimal condition. This entails things like voltage control by reactive power, frequency control by operating reserve, fault ride trough capability and so on. Many of those are naturally provided by large conventional power plants using synchronous generators like gas, nuclear or hydro. For inverter based systems, they have to be considered explicitly. For battery storage most are relatively easy to implement, some also in solar inverters. The tech exists, but yes, in some countries the regulations have not kept up with rapid expanse of inverter based power generation in the last years.
As always, there is a relevant xkcd for this: https://xkcd.com/2608/
This post and thread gives me (back) so much hope. I always hoped for something like described here. But I never came anywhere close and so I have lost the hope over time. I was thinking in the direction of “I just want someone to share my life with. It will work out to be ok somehow.” But some recent events and post like this give me back the hope to find a the person I really want to share time with. It also brings me the motivation to work on myself, so to be more like I would like to be. Thanks you all.
You got your units confused.
1 Watt = 1 J/s = 1 N m/s = 1 kg m^2 / s^3
Just moving things horizontally changes does not take energy (except for friction). But when we move something upwards, we move it against the surface acceleration of earth of g = 9.81 m/s^2. So we can say:
1 W ≈ 0,1 kg m/s
This means to store 1 kW, we would need to raise e.g. 1 ton with 0.1 m/s. So 1 minute of medium power cooking (1 kW), corresponds to lifting 1 ton approximately 6 meters.