OK, sorry to get off the track here. It's common to use a battery as a VR. Question is does the voltage increase as you rev the engine? If not, you're got a bad rectifier leg, bad charge coil, (I doubt it) or wiring problem.
Next question is how to hook both coils together. As Pardue states, you have two options, parallel or series. My question to him was; is it possible to parallel two AC sources? I ask that, because I see of no way for you to ensure your charge coils are 180 degrees out of phase with each other.
That experiment was done on a Tecumseh system and it didn't work. You generally can not parallel AC sources. However, you can parallel DC (rectified AC) to a common voltage regulator.
I don't think you can run your AC outputs in series, and if you ran your DC in series, you are looking at way more voltage than you want to charge your battery with. Could be as much as 40 VDC. That's why I asked the question of Pardue. (and why you'd need a VR)
I see Honda offers an extra coil as an option. I cant find a schematic for it though.