Replace transformer with PWM control
I would not recommend that: it would result in enormous power wastage. The reason being, during the on part of the PWM, the circuitry (and cables, component leads etc) between the mains supply and the capacitor would be acting basically as a (very low value) resistor which would dissipate the heat. For example, the approximate average voltage across the MOSFET/cables/rectifier would be 200v. In other words, very inefficient. Lastly, There would have to be a current-limiting feature controlling the MOSFET, otherwise the surge in current would also blow fuses, because in essence it would just be one giant short circuit.

But yes, regarding the peak current through the MOSFET, the MOSFET will have graphs and other specs which will define separately, the peak current (for example over extremely short pulses) as well as a total power dissipation which if the MOSFET is pulsed on and off could essentially be doubled for your purposes. But calculations would have to take into account the effectiveness of what heatsink you have etc.