I think you're still misunderstanding the point here.
A resistive load does not store power. The problem is that ANY mosfet implementation- be it a NMOS, PMOS, or a bizzare combination of them- allows current to flow either direction when vgs is greater than the threshold voltage.
So you may be trying to charge a 12v battery or cap with a 12v AC motor, which means 17v peak. OK, so the battery charges for the portion of the signal where Vmotor>12v. But what happens when the AC signal swings back towards zero? As soon as it goes below 12v, the battery or cap will discharge its power back into the power source. A diode will not do this. I see one of the schematics included a blocking diode after the rectifier. Nice but this will drop 0.7v which is half the problem we wanted to avoid in the first place.
The ideal diode is realized by putting an amp on Vds, when it is in the desired direction we turn on the gate. Some forward threshold is still essential since if Vds is driven to 0 then the circuit will either turn itself off when it should be on, or if there's a positive offset error, may never turn off even when the current goes the wrong direction.
The PMOS can be switched by simply looking if the source is + or -, but then NMOS must be switched by looking at the direction current will flow. Then the NMOS don't have much risk of turning on at the same time, though the PMOS do. Or you could build the fullwave rectifier as before and make the "ideal diode" on the output, then you only have to build 1 but it's an extra transistor. It will bring back the problem of the NMOS turning on at the same time though.