Storing the charge from a MOSFET Bridge Rectifier

Use a single schottky diode at the output.

You could use a dual schottky on the AC terminals and take the + DC out from the CT of the dual diode.This means that the P chan fets are not needed.The p chan fets have higher RDs on and are more expensive .I have implemented something similiar on a 12V 8A battery charger that had 6 3300microfarad electros across the unreg DC bus that was nominaly 19V. What been stated so far will be reliable for your job . If your input volts are very low you may have to sense DS volts and turn off the gate when current tries to run back .A jargon term for this is a "FIODE",In other words you want the fet to be a low drop diode .I have done this on a mains bridge using some small BJTs hung around the fets.