The problem you describe seems to be one targeted by the TerraPower project in Wyoming. It plans to operate at 100% capacity at all times (345 MWe), but makes itself more akin to other renewables by incorporating energy storage into its design.
It is supposed to be able to increase capacity to 150% (500 MWe), allowing it to respond to energy scarcity. But it can also respond to energy abundance by storing excess production in molten salt storage tanks.
