I like the idea of a capacitor, but I think it would be more feasible with a battery bank, because of the cost of the capacitor
If I take the numbers of 356 Volts, 1000 amps and 10 minutes, you get 213.6 MegaJoules! (59.3 kW-h). That is a lot of energy! but if you continu with those numbers and try to figure out the capacitor you need, it is going to be huge
At 1000 Volts, you need 427.2 Farads. That is not going to be cheap, even with supercapacitor. But you could have 50x 12Volts lead-acid batteries with 100 amps/hour each and you would get those 60kW-h that you need. (You would actually need more because you cannot take a battery down to 0% charge)
Anyway, this would only be feasible in some sort of power station. You would go to the "Electrical-fuel" station where they would have this capacity to fast-recharge your car. My guess is that it would still take a long time to charge it at your house, unless you have a lot of money to spend on a special charger with a 200+MegaJoules capacitor bank in it.