The coils will give outputs in different phase relationships to each other; any linking will reduce the output
You can use two bridge rectifiers, one connected to the ends of each of the two separate windings.
Then parallel the DC terminals of the bridge rectifiers.
That should give a four pulse per cycle waveform that requires rather less smoothing, as well as only needing two wires.
Use suitably rated schottky diodes for the bridge rectifiers if you want the bet possible efficiency; they have significantly lower voltage drop than conventional diodes.