Capacitors have a maximum voltage they can hold as you say, but also have a maximum current they can handle. This is usually referred to as the ripple current spec. Since it's the current that matters, it can also be expressed as a maximum AC voltage at particular frequencies.
In your case, you will have a 424V1200V p-p 70 kHz sine wave on your capacitor. The fastest rate of change of that signal is at the zero crossing, which is 424V600V * 2 * Pi * 70kHz = 186264 V/µs. The current thru a capacitor is dV/dt * C. Let's use 1 µF for example. 186 264 V/µs * 1µF = 186264 Amps peak, 132187 Amps RMS, which is the ripple current the cap must be able to sustain.