I don't doubt that there will be a technical way to solve all these problems, whether with batteries, or with creating methane on periods with high energy, and burning it on periods with low energy, or with just simply.
But there is one very high problem:
Traditional energy resources will always be cheaper. Simple as that.
Your fanciest battery technology won't make the actual price you pay for energy from renewable resources cheaper than the extraction costs for fossile energy sources. And if that isn't provided, the owners of the gas and oil fields will just simply provide energy at a lower price than yours, and will still get customers. And you can be the greenest guy ever, if your neighbour country burns all the fuel now, because you aren't interested in buying it anymore, you haven't won a thing for the planet.
There is no other way to limit global carbon production than by creating a global cap for carbon output, and by enforcing that cap.