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.
Yep, Inrush is killing you, that is a lot of bulk capacitance to have without any inrush limiting. Assuming a trace resistance of 100mOhm, and that your 6 or 14 electrolytic capacitors in parallel will have ~ 0 ohm impedance, your instant current is 160A on startup. Here is a nice site for looking at this.
MustCalculate
Most large capacitance banks have huge diodes and Capacitors designed to stand the inrush, or some form of inrush limiting, passive or active. A cheep passive solution is a NTC resistor, they are sold for this exact purpose, here are some on digikey: Here. You place them in series with the bank and the input voltage, as they heat up the resistance goes down.
Update:
I'll also add if you choose to go this route, notice the NTC's are rated for maximum capacitive load and approximate steady state current. The loading is usually for 120 and 240V but this can be adjusted to your ~16VAC easily. Since the important property is power dissipation, the difference is squared. for example:
a device rated for 500uF@240VAC will handle 2000uF@120VAC or 8000uF@60VAC. Notice the voltage difference is squared.
Also Note:
This method is only effective if the device is not powered on and off quickly in succession. The NTC must have time to cool back down to room temperature otherwise when you flip the power back on, the resistance will still be low and your diodes could go poof again. Typically they take less then a minute to cool off. That being said, they will still provide some protection even when hot, as they still have a lot more resistance then a PCB trace.
Best Answer
The diode rating is for the part itself. The manufacturer states that the part is rated for 3A for each part, so you shouldn't exceed 3A. There is some judgement in this statement, meaning that you can exceed the rating without damaging the part for short periods, but not for long periods.
A bridge rectifier uses 4 of these, two of which are conducting at a time. This means that if the bridge rectifier is seeing an RMS current of 3A, then each diode is experiencing an RMS current of 1.5A. So to answer your question, yes, your rating could be considered increased over that of the individual components.
Having said that, a 2x safety margin is a good thing in power electronics. If you need 3A continuous output, I would recommend a 5A or higher diode.