I hope I don't reveal my ignorance with this question, but here goes. How can the voltages be additive when they are 120 degrees out of phase?
With a bridge rectifier they're only 60 degrees out of phase. Add a capacitor and the phase doesn't matter a lot and you just add the voltage - minus the capacitor droop since they're not in phase. When a coil is in the part of the phase where the voltage output is under about 1.2v the diodes bypass the current from the others around it.
But at the frequencies and currents we're running you need ENORMOUS capacitors - or the droop is so large they might as well not be there.
Series means you have 12, rather than 2, diodes in series dropping about an extra 2.4 volts. And the diodes are conducting all the time, resulting in about three times the heating on the diode and requiring bigger diodes and heatsinks. (The two effects are related.)
The proposal to half-wave rectify the system doesn't work well at all. If you don't put in bypass diodes or capacitors you get nothing, period. If you do put them in, you're still getting less than half the power from the coils compared to full-wave even in the best of cases - and still have extra diode drop.
You REALLY don't want to put separately-recitfied phases in series unless there's no other way to get power from them.