EVs could come with a spare battery, that way the spare can be charged during peak production. When you get home you replace the spent one in the car with the charged one. That way it also solves the long charging time problem.
Coal and nuclear can ramp up within minutes (hydro within seconds). So coal can adapt as long as the changes isn't too sudden (and unforeseen). Sunset and sunrise can be predicted very accurately, you can probably also predict how the cloud cover will change over the solar panels the next 20 minutes or so that would be necessary to make adjustments in advance.
The fuel pebbles in the pebble bed reactor use graphite as moderator, but the pebbles are encapsulated in silicon carbide which prevents the possibility of them catching fire. The reactor is self moderated and will not go above about 2000 C even if cooling fails, which the structure can deal with. No risk of steam explosions or buildup of hydrogen like you have in a water cooled reactor. If it's helium cooled, the helium is inert and also prevents any chance of fire. Helium can't chemically decompose into a stoichiometric mixture of H
2 and O
2 like water can. I've read that the german THTR reactor had some problems that made it uneconomical but there are other successful pebble bed reactors in the world. Anyway, I trust the nuclear physicists can figure out what is the best design.
Just read about a nice Canadian reactor design called slowpoke-3, that seems very safe and was intended to provide district heating, unfortunately anti-nuclear protests killed that one as well. Much nicer with a good old cosy coal furnace apparently.