Heating and transport are the easiest in that regard. Most trucks drive during the day have the driver resting during the night. At night there's little demand, but wind and nuclear continue generating, so from a grid standpoint that's the perfect time to charge all the trucks. Cars can similarly be mostly charged during the night, as that's when they are at home. Heat demand is more variable, but heat is much easier to store than electricity itself. Everyone with a boiler already has a heat store at home. If you make the boiler a bit larger you can configure it to only heat when there's excess electricity (typically the night or at peak solar power around noon). And that's before you start with more efficient heat storage devices, like heating sand instead of water.

All of those solutions require infrastructure investments and smarter grids (likely with real-time pricing to incentivize consumers to use power when there's an excess, and an API so devices like chargers and boilers can act on this information without user input). But they don't require power storage at the grid level.