> The amount of lithium it would take to handle an unusually cloudy week would be astronomical.

Unusual events shouldn't be handled by high capex, high efficiency storage. They should be handled by lower capex, lower round trip efficiency storage (as should long term/seasonal storage).

I will once again point to Standard Thermal.

https://www.standardthermal.com/

https://www.orcasciences.com/articles/standard-thermal-copy

https://austinvernon.site/blog/standardthermal.html

Ten cents per kWh of storage capacity!