Re: 350kW!!!!
This is solved more by the Economy-7 type approach.
You will be able to choose the priority of charge. Fast charge for now and pay standard rates or take a slow trickle when the grid wants to dump electricity and just tell the smart charger then you need the charged vehicle by it then turns into a very predictable supply and demand situation.
The modelling of stress on the grid is getting pretty sophisticated even at hyper local levels - it won't be perfect but it will work in the end with some experience of it going wrong.
It will be mandated that vehicle chargers will be voltage drop limited to prevent brown outs. That is pretty easy to do.