This is completely backwards. Demand is highly price inelastic and inversely correlated with the supply of renewables. People usually eat at night. They heat their homes overnight. None of these things will change based on energy prices.
What you're proposing is a tax on the poor, and no practical benefit to boot.
> The charger for your electric car is another very practical sink for cheap electricity.
I don't have an electric car. I do not know anybody with an electric car. And wouldn't the surplus show up specifically when those cars aren't at the home?
> A battery consisting of a pile of rocks can't be expensive.
No, but the labor cost of hooking up your pile of rocks battery will be impractical for almost everyone.
> The next level is using residential HVAC systems the same way.
Again, I don't know anybody with an HVAC system. Everything here in the UK is based on natural gas and would cost an unbelievable amount of money to replace with electric.