I really hope these kinds of things start to increase in popularity, but I think it needs more government intervention for it to happen.
It would probably help if they mandated smart electric storage heaters on new builds but beyond that I'm not sure you need to do much more.
You can rely on people's self interest to buy a new washing machine that saves them money, for instance.
Also, since green tech often saves fewer actual dollars from a consumer's pocket than the "real" cost of the externalities saved, subsidies and/or eco-friendly certification would also be good.
The obvious solution to this is grid frequency. It's already a requirement for solar grid tie invertors for example.
The company I work for has two plants near each other, where one is run in winter, and one in summer, each producing a different product. The workers alternate between which plant they work at depending on the season. The other plant is shutdown for maintenance. By replacing the conveyor belt every year we ensure production never shuts down unexpectedly while people are working, and this more than makes up for the cost of a factory that is idle half of the year.
We have a lot of factories. The above two plants are not the foundry where we pour iron which I talked about in a different thread.
It clearly doesn't matter what percentage of the input cost is energy to whether the plant is profitable. So long as that percentage is non-zero there will always be an energy cost at which the total cost to produce is higher than the market price to sell (ask any industry in Texas).
Clearly there are other factors too, in your example it seems like labour costs are very high or perhaps contractual demands on output mean down time is unacceptable.
The reason an idle machine is bad is because you have to pay interest on the loan (write downs and all that complexity). You also have to pay rent (taxes) on the building they are in. You need to do basic maintenance (HVAC so they don't deteriorate). You need to ensure the machine operator (which might be a rare skill) is available when you put it back to work, which might mean paying the operator to do nothing just so he doesn't find a new job while laid off. All of these raise the input cost of restarting after a long period of being idle - sometimes you are better off scraping the machines and buying new if you need them.
Against that you have demand and ability to store the finished product. Some things can be stored up (just in time calls this bad, but it isn't always a bad thing), while others degrade quickly. Some things your customers will order well in advance so you can plan around demand, while others you get an order for "yesterday" (if only you had a time machine).
Depending on how all of the above work out idle factories have different economics.
Rather than wondering how we can store all the excess capacity it's probably more cost effective to wonder how we can shift demand.
Aluminum smelters in Germany use gargantuan amounts of electricity, for instance, but they can use 3x as much on Friday when power is cheap than Monday when it's not with relative ease.
Using a powerwall to keep production steady would be a ridiculous waste of money.
Storage heaters need to make a comeback, as well.