First the capacitor will be fine on 120hz ripple, it was designed for optimum power factor/for capacitive reactance on 60hz AC, you will be using DC ripple.
But I question the method of control, it would probably be much more economical to build a 4 quadrant SCR drive, this would be connected across the incoming supply without any need to reduce the voltage or build a power supply.
Either way, if you need 12v for logic supply, why not use a simple supply like a wall-wart type etc, if necessary add a 12v regulator.
Al.


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