There is no power factor correction with a _generator_ (or rather an alternator, for AC), regardless of how its constructed.
With no load, the alternator produces voltage - but there is no current. No current means no current phase relationship to measure.
When you connect loads to it, the phasing of the load current is the sum of all the power factors of the loads; some may lead and some may lag.
It's the loads that needs correction (if not resistive), not the alternator.
If you are meaning you want to rectify the alternator output efficiently, then a switch mode PSU with power factor correction would presumably be suitable.
However at the scale of the microwave oven motor, it's efficiency gains is likely zero or negligible.
Another approach would be in effect use a three phase PWM inverter circuit, as you would use to drive the motor, but continuously running in peak "regenerative braking" mode.
If I remember right, that's the point where the back EMF of the motor would be half that of the speed you are "braking" from; ie. if you have 240V back emf (output) you set the pwm to the percentage it would be at when driving the motor in the same direction with a back EMF of 120V.
That gives you the maximum possible braking force, which is the point the mechanical to electrical power conversion is at its peak.
The regenerated power is returned to the DC bus that is nominally feeding the output bridge, if the inverter was being used to drive the motor.