It appears that you wire the power coils in series, and I'd suggest a hall sensor instead of a reed switch ... the reed will fail quickly due to back EMF spikes/arcs. The pickup coils - I'd use #26 wire and nearly fill each former. I believe they are each wound the same. Use a potentiometer and TIP33 to switch the power coils .. via the hall sensor output.
For the alternator windings, I'd imaging you'd wire it as a 3 phase motor and all coils in the same direction. Alternate the alternator rotor magnets north/south/north/south on both of them. If you want 3 phase AC output then omit the rectifier. Use the 2nd phase as a center tap.