Sorry Tesla, but you're about 200 miles short on the car's range. That's a notable achievement, no doubt, but if you want to sell a car to Joe Public based on it cross-country capabilities then you need to provide a battery that will last for an entire day of driving at highway speeds before needing to be recharged (i.e. 8-10 hours behind the wheel). That means around a 500 mile range. I for one wouldn't bother driving cross country if I couldn't do at least 500 miles between when I woke up and when I had to turn in for the night (i.e. charge the car fully overnight). And that's not counting the times I've driven non-stop in shifts with other drivers and done well over 500 miles. For any gas car this pretty much means more than 1 tank per driving day, but when filling takes all of 5 minutes, so it's a non-issue. That kind of range won't really be possible with EVs until Sodium-air batteries or some other type of metal-air battery makes super high capacity batteries cheap and light enough to bring to the masses. The bottom line is that EVs will remain a niche market until advancements in battery technology bring down the costs enough to be competitive with gasoline or diesel powered cars of equivalent range, if not equivalent refueling time. Anything less is not 'progress'. That's why hydrogen fuel cell cars, at least on this front, have more 'promise' in the sense that you get the same sort of range and refueling time vs today's gasoline cars. I won't get into the myriad of other issues with hydrogen fuel cell cars here though.
It's called PSH (pumped storage hydroelectricity) and it's the only way to store large amounts of energy for later consumption at an even remotely reasonable cost. Basically it involves running a turbine hydroelectric generator in reverse to pump water uphill to a reservoir during off peak hours and then run the turbine off of that water during peak times for load balancing. Since nuclear and coal based power plants can't be ramped up or down quickly to match demand, pumped storage hydro is used to soak up a lot of the excess capacity that's unused during off peak hours. Obviously you're paying for the inefficiencies of turbine power generation, but they're pretty good (70-80%) and the differences in peak vs off peak pricing more than make up for this cost. No battery bank in existence can even come close to matching the amount of potential energy that can be stored in a reservoir dollar for dollar. That's probably why it accounts for more than 99% of global bulk storage capacity.