Interesting, wonder what the hard limits on voltage are? 350 amps @ 1000V must have one hell of a cord! Would be interesting to see what this station looks like.
Type "Electrify America" into Google and hit the images tab. The majority of their 788 sites include one or more 350 kW stations. The cords are probably over an inch thick, I've never measured, but no thicker than a fuel hose for a gas pump. They're liquid cooled to carry that current without overheating.